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Journal articles on the topic 'Integral transforms'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 August 2024

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1

Aghili, Arman. "Non-homogeneous impulsive time fractional heat conduction equation." Journal of Numerical Analysis and Approximation Theory 52, no. 1 (July 10, 2023): 22–33. http://dx.doi.org/10.33993/jnaat521-1316.

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This article provides a concise exposition of the integral transforms and its application to singular integral equation and fractional partial differential equations. The author implemented an analytical technique, the transform method, for solving the boundary value problems of impulsive time fractional heat conduction equation. Integral transforms method is a powerful tool for solving singular integral equations, evaluation of certain integrals involving special functions and solution of partial fractional differential equations. The proposed method is extremely concise, attractive as a mathematical tool. The obtained result reveals that the transform method is very convenient and effective.Certain new integrals involving the Airy functions are given.

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2

Mohammed, Nada Sabeeh, and Emad A. Kuffi. "The complex integral transform complex Sadik transform of error function." Journal of Interdisciplinary Mathematics 26, no. 6 (2023): 1145–57. http://dx.doi.org/10.47974/jim-1613.

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Recently, the focus of mathematics scientists on the use of integral transforms in solving problems in various fields such as engineering, science, and other scientific fields has led to the need to know the integral transforms of the error function in order to evaluate improper integrals. In this paper, we will use transform (complex Sadik transform) and prove its ability to evaluate improper integrals that have error functions.

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3

Sharma, M. D., and S. Nain. "Numerical evaluation of inverse integral transforms: Dynamic response of elastic materials." International Journal of Engineering, Science and Technology 12, no. 2 (June 1, 2020): 29–34. http://dx.doi.org/10.4314/ijest.v12i2.4.

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This study discusses the use of numerical integration in evaluating the improper integrals appearing as inverse integral transforms of non-analytic functions. These transforms appear while studying the response of various sources in an elastic medium through integral transform method. In these studies, the inverse Fourier transforms are solved numerically without bothering about the singularities and branch points in the corresponding integrands. References on numerical integration cited in relevant papers do not support such an evaluation but suggest contrary. Approximation of inverse Laplace transform integral into a series is used without following the essential restrictions and assumptions. Volume of the published papers using these dubious procedures has reached to an alarming level. The discussion presented aims to draw the attention of researchers as well as journals so as to stop this menace at the earliest possible.Keywords: Inverse Fourier transforms, inverse Laplace transforms, Romberg integration, improper integral, elastic waves

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Salamat, Kaushef, and Nousheen Ilyas. "DUALITIES BETWEEN FOURIER SINE AND SOME USEFUL INTEGRAL TRANSFORMATIONS." Journal of Mathematical Sciences & Computational Mathematics 2, no. 4 (July 5, 2021): 542–63. http://dx.doi.org/10.15864/jmscm.2408.

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The most useful technique of the mathematics which are used to finding the solutions of a lot of problems just like bending of beam, electrical network, heat related problems, which occurs in many disciplines of engineering and sciences are the techniques of integral transforms. In our research I discussed the duality between Fourier Sine transforms and some others effective integral transforms (namely Laplace transform, Mahgoub transform, Aboodh transform and Mohand transform). To justify the scope of dualities relation between Fourier Sine transform and other integral transforms (that are mentioned above, I presented the tabular representation of integral transform (namely Laplace transform, Aboodh transform, Mohand transform and Mahgoub transform) of various used functions by using Fourier Sine and other integral transforms dualities relation to signify fruitfulness of such connections. Results showed that these integral transform are strongly related with Fourier Sine transform.

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5

Luchko, Yuri. "Some Schemata for Applications of the Integral Transforms of Mathematical Physics." Mathematics 7, no. 3 (March 12, 2019): 254. http://dx.doi.org/10.3390/math7030254.

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In this survey article, some schemata for applications of the integral transforms of mathematical physics are presented. First, integral transforms of mathematical physics are defined by using the notions of the inverse transforms and generating operators. The convolutions and generating operators of the integral transforms of mathematical physics are closely connected with the integral, differential, and integro-differential equations that can be solved by means of the corresponding integral transforms. Another important technique for applications of the integral transforms is the Mikusinski-type operational calculi that are also discussed in the article. The general schemata for applications of the integral transforms of mathematical physics are illustrated on an example of the Laplace integral transform. Finally, the Mellin integral transform and its basic properties and applications are briefly discussed.

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KABRA, SEEMA, and HARISH NAGAR. "INTEGRAL TRANSFORM OF K4-FUNCTION." Journal of Science and Arts 21, no. 2 (June 30, 2021): 429–36. http://dx.doi.org/10.46939/j.sci.arts-21.2-a10.

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In this present work we derived integral transforms such as Euler transform, Laplace transform, and Whittaker transform of K4-function. The results are given in generalized Wright function. Some special cases of the main result are also presented here with new and interesting results. We further extended integral transforms derived here in terms of Gauss Hypergeometric function.

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7

Kuffi, Emad A., and Eman A. Mansour. "Solving Partial Differential Equations Using the New Integral Transform “Double SEE Integral Transform”." Journal of Physics: Conference Series 2322, no. 1 (August 1, 2022): 012009. http://dx.doi.org/10.1088/1742-6596/2322/1/012009.

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Abstract The immense importance of differential equations and integral transforms in scientific fields leads to inducting the integral transforms as a solving tool for partial differential equations. The “double SEE integral transform” is a novel integral transform suggested in this research. Its properties and applicability to some functions have been studied, and the ability of the proposed transform to solve partial differential equations has been proven through a practical application.

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8

ZORICH, Anton. "INVERSION OF HOROSPHERICAL INTEGRAL TRANSFORM ON REAL SEMISIMPLE LIE GROUPS." International Journal of Modern Physics A 07, supp01b (April 1992): 1047–71. http://dx.doi.org/10.1142/s0217751x92004178.

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There exists the wonderful integral transform on complex semisimple Lie groups, which assigns to a function on the group the set of its integrals over "generalized horospheres" — some specific submanifolds of the Lie group. The local inversion formula for this integral transform, discovered in 50's for [Formula: see text] by Gel'fand and Graev, made it possible to decompose the regular representation on [Formula: see text] into irreducible ones. In case of real semisimple Lie group the situation becomes more complicated, and usually there is no reasonable analogous integral transform at all. Nevertheless, in the present paper we succeed to define the integral transforms on the Lorentz group and some other real semisimple Lie groups, which are in a sense analogous to the integration over "horospheres". We obtain the inversion formulas for these integral transforms.

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9

Gwila, Nbila, and Ali Farhat. "GF1 Integral Transform and its Some Applications." مجلة الجامعة الأسمرية: العلوم التطبيقية 7, no. 2 (June 30, 2022): 84–93. http://dx.doi.org/10.59743/aujas.7.2.2.

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One of the significant methods for solving initial value problems and some integral equations is the use of integral transforms which serve for converting them to algebraic equations that can be solved by applying the inverse transforms. Resently, several integral transforms have been presented and applied for solving initial value problems and some integral equations such as Sumudu, Natural, Al-Tememe, Elzaki, Aboodh, T Kashuri and Fundo, Mahgoub, Kamal, Polynomial, Al-Zughair, Rangaig, Mohand and, Al-Zughair Transforms. In this paper, integral transform has been presented and studied which is in a clase of Laplace integral transform and related to Jafari general integral transform. Furthermore, theorems and some applications for solving initial value problems have been provided.

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10

Campos, Harren, Jezer Fernandez, and Jade Bong Natuil. "On Degenerate Laplace-type Integral Transform." European Journal of Pure and Applied Mathematics 16, no. 4 (October 30, 2023): 2213–33. http://dx.doi.org/10.29020/nybg.ejpam.v16i4.4868.

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This paper is motivated by the work of Taekyun Kim and Dae San Kim on the degenerate Laplace transform and degenerate gamma function, as published in the Russian Journal of Mathematical Physics. We introduce the degenerate Laplace-type integral transform and delve into its properties and interrelations. This paper focuses on the degenerate Laplace-type integral transforms of several fundamental functions, including the degenerate sine, degenerate cosine, degenerate hyperbolic sine, and degenerate hyperbolic cosine functions. Furthermore, we establish crucial connections between the degenerate Laplace-type integral transform and existing degenerate integral transforms. Specifically, we explore its relationships with the degenerate Laplace transform, the degenerate Elzaki transform, and the degenerate Sumudu transforms.

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11

Man'ko, Margarita A. "Propagators, Tomograms, Wavelets and Quasidistributions for Multipartite Quantum Systems." Open Systems & Information Dynamics 14, no. 02 (June 2007): 179–88. http://dx.doi.org/10.1007/s11080-007-9046-2.

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Integral transforms of analytic signal and quantum-system states like wavelets, tomograms, Ville-Wigner and other quasidistributions are constructed for systems with several degrees of freedom. Mutual relations of the integral transforms are presented. Quantum propagator is interpreted as the kernel of the integral transform. An example of the integral transforms with generic Gaussian kernels is studied. The fractional Fourier transform is discussed.

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12

Bhandari, Piyush Kumar, and Sushil Kumar Bissu. "Inequalities for some classical integral transforms." Tamkang Journal of Mathematics 47, no. 3 (September 30, 2016): 351–56. http://dx.doi.org/10.5556/j.tkjm.47.2016.1981.

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By using a form of the Cauchy-Bunyakovsky-Schwarz inequality, we establish new inequalities for some classical integral transforms such as Laplace transform,Fourier transform, Fourier cosine transform, Fourier sine transform, Mellin transform and Hankel transform.

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13

Inayat‐Hussain, A. A. "Mathieu integral transforms." Journal of Mathematical Physics 32, no. 3 (March 1991): 669–75. http://dx.doi.org/10.1063/1.529409.

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14

Khan, Sana Ullah, Asif Khan, Aman Ullah, Shabir Ahmad, Fuad A. Awwad, Emad A. A. Ismail, Shehu Maitama, Huzaifa Umar, and Hijaz Ahmad. "Solving nth-order Integro-differential Equations by Novel Generalized Hybrid Transform." European Journal of Pure and Applied Mathematics 16, no. 3 (July 30, 2023): 1940–55. http://dx.doi.org/10.29020/nybg.ejpam.v16i3.4840.

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Recently, Shehu has introduced an integral transform called Shehu transform, which generalizes the two well-known integrals transforms, i.e. Laplace and Sumudu transform. In the literature, many integral transforms were used to compute the solution of integro-differential equations (IDEs). In this article, for the first time, we use Shehu transform for the computation of solution of $n^{\text{th}}$-order IDEs. We present a general scheme of solution for $n^{\text{th}}$-order IDEs. We give some examples with detailed solutions to show the appropriateness of the method. We present the accuracy, simplicity, and convergence of the proposed method through tables and graphs.

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15

Chaudhary, Priti, Pawan Chanchal, Yogesh khandelwal, and Hoshiyar singh. "Duality of “Some Famous Integral Transforms” From the Polynomial Integral Transform." International Journal of Mathematics Trends and Technology 55, no. 5 (March 25, 2018): 345–49. http://dx.doi.org/10.14445/22315373/ijmtt-v55p545.

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16

Bandyopadhyay, Dwiptendra. "General integral transform – its convergence and consequences." Boletim da Sociedade Paranaense de Matemática 40 (February 5, 2022): 1–9. http://dx.doi.org/10.5269/bspm.51690.

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Objective of this study is to give a shape of general integral transform for studying its convergence in the general set-up, from which convergences of some well know integral transforms follow easily as well as these integral transforms appear as particular cases of the present integral transform; some more may appear as new but special cases of present transform which have been listed but not studied here.

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17

Xhaferraj, Ervenila Musta. "The New Integral Transform: “NE Transform” and Its Applications." European Journal of Formal Sciences and Engineering 6, no. 1 (April 1, 2023): 22–34. http://dx.doi.org/10.2478/ejfe-2023-0003.

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Abstract This work introduces a new integral transform for functions of exponential order called “NE integral transform”. We prove some properties of NE -transform. Also, some applications of the NE- transform to find the solution to ordinary linear equation are given. The relationships of the new transform with well-known transforms are characterized by integral identities. We study the properties of this transform. Then we compare it with few exiting integral transforms in the Laplace family such as Laplace, Sumudu, Elzaki, Aboodh and etc. As well, the NE integral transform is applied and used to find the solution of linear ordinary differential equations.

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18

Kashiwara, Masaki, and Pierre Schapira. "Integral transforms with exponential kernels and Laplace transform." Journal of the American Mathematical Society 10, no. 4 (1997): 939–72. http://dx.doi.org/10.1090/s0894-0347-97-00245-2.

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19

De Bie, H. "Fourier transform and related integral transforms in superspace." Journal of Mathematical Analysis and Applications 345, no. 1 (September 2008): 147–64. http://dx.doi.org/10.1016/j.jmaa.2008.03.047.

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20

Rodrigo, Marianito R., and Mandy Li. "Analogues of the Laplace Transform and Z-Transform with Piecewise Linear Kernels." Foundations 1, no. 1 (September 13, 2021): 99–115. http://dx.doi.org/10.3390/foundations1010008.

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Two new transforms with piecewise linear kernels are introduced. These transforms are analogues of the classical Laplace transform and Z-transform. Properties of these transforms are investigated and applications to ordinary differential equations and integral equations are provided. This article is ideal for study as a foundational project in an undergraduate course in differential and/or integral equations.

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21

Saadeh, Rania. "A Generalized Approach of Triple Integral Transforms and Applications." Journal of Mathematics 2023 (March 6, 2023): 1–12. http://dx.doi.org/10.1155/2023/4512353.

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In this study, we introduce a novel generalization of triple integral transforms, which is called a general triple transform. We present the definition of the new approach and prove the main properties related to the existence, uniqueness, shifting, scaling, and inverse. Moreover, relations between the new general triple transform and other transforms are presented, and new results related to partial derivatives and the triple convolution theorem are established. We apply the general triple transform to solve some applications of various types of partial differential equations. The strength of the new approach is that it covers almost all integral transforms of order one, two, and three, and hence no need to find new formulas of triple integral transforms or to study the basic properties.

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22

Ma, Guangsheng, Hongbo Li, and Jiman Zhao. "Windowed Fourier transform and general wavelet algorithms in quantum computation." Quantum Information and Computation 19, no. 3&4 (March 2019): 237–51. http://dx.doi.org/10.26421/qic19.3-4-4.

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In this paper, we define the quantum windowed Fourier transform and study some of its properties, then we develop two useful operations called quantum convolution and `integral'. Quantum `integral' allows us to implement the integral transforms quantum-mechanically with a certain probability, including general wavelet kernel transforms. Furthermore, we propose an improved wavelet kernel transform for quantum computation.

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23

Yürekli, O. "Identities on fractional integrals and various integral transforms." Applied Mathematics and Computation 187, no. 1 (April 2007): 559–66. http://dx.doi.org/10.1016/j.amc.2006.09.001.

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24

Jain, Pankaj, Sandhya Jain, and Vladimir Stepanov. "LCT BASED INTEGRAL TRANSFORMS AND HAUSDORFF OPERATORS." Eurasian Mathematical Journal 11, no. 1 (2020): 57–71. http://dx.doi.org/10.32523/2077-9879-2020-11-1-57-71.

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25

Güngör, Nihan. "Solution of Convolution Type Linear Volterra Integral Equations with Formable Transform." International Journal of Latest Technology in Engineering, Management & Applied Science 11, no. 12 (2022): 08–11. http://dx.doi.org/10.51583/ijltemas.2022.111202.

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The integral transforms have recently been the focus of the studies, because the integral transforms provide simple and minimal computations for solving complicated problems in engineering and science. In this study, the Formable transform is utilized to solve convolution type linear Volterra integral equations of the first kind and the second kind. Several examples are offered to illustrate the Formable transform approach for solving convolution type Volterra integral equations.

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26

Chang, Seung Jun, Hyun Soo Chung, and Jae Gil Choi. "Sequential transforms associated with Gaussian processes on function space." International Journal of Mathematics 27, no. 04 (April 2016): 1650031. http://dx.doi.org/10.1142/s0129167x16500312.

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We define two generalized sequential transforms on the function space [Formula: see text]. In order to find the essential structure of the generalized sequential transforms we first investigate the relationships between the generalized analytic [Formula: see text]-Feynman integral and the generalized [Formula: see text]-function space integral. We then establish the existences of our sequential transforms on [Formula: see text]. One of these sequential transforms identifies the generalized analytic [Formula: see text]-Fourier–Feynman transform and the other transform plays a role as an inverse transform of the generalized analytic [Formula: see text]-Fourier–Feynman transform.

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27

Chung, Hyun. "An integral transform via the bounded linear operators on abstract wiener space." Filomat 37, no. 17 (2023): 5541–52. http://dx.doi.org/10.2298/fil2317541c.

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In this paper, we obtain some results of a more rigorous mathematical structure that can guarantee the orthogonality of an orthogonal set even when results and formula on abstract Wiener integrals or some transforms using bounded linear operators. We then establish the existence of an integral transform on abstract Wiener space. Finally, we obtain some fundamental formulas with respect to the integral transform involving the Cameron-Storvick type theorem.

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28

Milovanovic, Gradimir, Rakesh Parmar, and Arjun Rathie. "A study of generalized summation theorems for the series 2F1 with an applications to Laplace transforms of convolution type integrals involving Kummer's functions 1F1." Applicable Analysis and Discrete Mathematics 12, no. 1 (2018): 257–72. http://dx.doi.org/10.2298/aadm171017002m.

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Motivated by recent generalizations of classical theorems for the series 2F1 [Integral Transform. Spec. Funct. 229(11), (2011), 823-840] and interesting Laplace transforms of Kummer's confluent hypergeometric functions obtained by Kim et al. [Math. Comput. Modelling 55 (2012), 1068-1071], first we express generalized summations theorems in explicit forms and then by employing these, we derive various new and useful Laplace transforms of convolution type integrals by using product theorem of the Laplace transforms for a pair of Kummer's confluent hypergeometric function.

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29

Eltayeb, Hassan, Adem Kılıçman, and Ravi P. Agarwal. "On Integral Transforms and Matrix Functions." Abstract and Applied Analysis 2011 (2011): 1–15. http://dx.doi.org/10.1155/2011/207930.

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The Sumudu transform of certain elementary matrix functions is obtained. These transforms are then used to solve the differential equation of a general linear conservative vibration system, a vibrating system with a special type of viscous damping.

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30

Sánchez-Perales, Salvador, Francisco J. Mendoza Torres, and Juan A. Escamilla Reyna. "Henstock-Kurzweil Integral Transforms." International Journal of Mathematics and Mathematical Sciences 2012 (2012): 1–11. http://dx.doi.org/10.1155/2012/209462.

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31

Petrov, V. E. "Generalized Trigonometric Integral Transforms." Journal of Mathematical Sciences 224, no. 1 (May 18, 2017): 135–49. http://dx.doi.org/10.1007/s10958-017-3400-x.

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32

Taha, Nidal, R. Nuruddeen, and Abdelilah Sedeeg. "Dualities between ''Kamal & Mahgoub Integral Transforms'' and ''Some Famous Integral Transforms''." British Journal of Applied Science & Technology 20, no. 3 (January 10, 2017): 1–8. http://dx.doi.org/10.9734/bjast/2017/32380.

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33

BATOOL, SAIMA, GHULAM FARID, and SADIA KOUSAR. "SOME INTEGRAL TRANSFORMS INVOLVING GENERALIZED BESSEL-MAITLAND FUNCTION." Journal of Science and Arts 23, no. 3 (September 30, 2023): 681–92. http://dx.doi.org/10.46939/j.sci.arts-23.3-a09.

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In this paper, we establish some results in terms of generalized Wright hypergeometric function by applying different integral transforms such as Laplace transform, Whittaker transform, Hankel transform, K-transform, Sumudu transform, fractional Fourier transform etc. on the generalized Bessel-Maitland function.

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34

Suthar, Dayalal, Sunil Dutt Purohit, Haile Habenom, and Jagdev Singh. "Class of integrals and applications of fractional kinetic equation with the generalized multi-index Bessel function." Discrete & Continuous Dynamical Systems - S 14, no. 10 (2021): 3803. http://dx.doi.org/10.3934/dcdss.2021019.

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<p style='text-indent:20px;'>In this article, we have investigated certain definite integrals and various integral transforms of the generalized multi-index Bessel function, such as Euler transform, Laplace transform, Whittaker transform, K-transform and Fourier transforms. Also found the applications of the problem on fractional kinetic equation pertaining to the generalized multi-index Bessel function using the Sumudu transform technique. Mittage-Leffler function is used to express the results of the solutions of fractional kinetic equation as well as its special cases. The results obtained are significance in applied problems of science, engineering and technology.</p>

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35

Khalouta, Ali. "A new exponential type Kernel integral transform: Khalouta transform and its applications." Mathematica Montisnigri 57 (2023): 5–23. http://dx.doi.org/10.20948/mathmontis-2023-57-1.

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In this paper, we suggest a new integral transform called the Khalouta transform, which is a generalization of many integral transforms having exponential type kernel. We discuss certain results on the inverse and the existence of this integral transform. We present useful properties of the Khalouta transform and their applications to solve differential equations. Furthermore, we prove the duality between the Khalouta transform and other transforms such as the Laplace-Carson transform, Sumudu transform, ZZ transform, ZMA transform, Elzaki transform, Aboodh transform, Natural transform and Shehu transform. Finally, we ensure the efficiency and accuracy of the Khalouta transform by solving various examples of both ordinary, integro and partial differential equations.

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36

N. O., Onuoha. "Kamal Transform of Unit Step Functions." African Journal of Mathematics and Statistics Studies 7, no. 3 (July 12, 2024): 1–8. http://dx.doi.org/10.52589/ajmss-a8vkkqoa.

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This research presents the Kamal transform of unit step functions. Kamal transform is an integral transform that can be applied to solve mathematical problems. Kamal transform has some similarities with Laplace transform. Both transforms are half line and one fold integral transforms. Due to the applications of unit step functions in diverse areas, this paper showcases the Kamal transform of unit step functions. We applied Kamal transform to the following unit step functions: (a) Heaviside unit step function, (b) Shifted unit step function, and (c) Unit impulse function. The results obtained showed that the new integral transform (Kamal transform) can be applied to unit step functions.

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37

Ricci, P. E., and G. Mastroianni. "ERROR ESTIMATES FOR A CLASS OF INTEGRAL AND DISCRETE TRANSFORMS." Studia Scientiarum Mathematicarum Hungarica 36, no. 3-4 (December 1, 2000): 291–306. http://dx.doi.org/10.1556/sscmath.36.2000.3-4.1.

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We consider a class of integral transforms which generalize the classical Fourier Trans- form.We erive some theoretical error bounds for the corresponding approximate iscrete transforms,inclu ing the Discrete Fourier Transform.

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38

Aylikci, Fatih, Nese Dernek, and Gulesin Balaban. "New identities on some generalized integral transforms and their applications." Filomat 36, no. 9 (2022): 2947–60. http://dx.doi.org/10.2298/fil2209947a.

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In this paper the authors gave an iteration identity for the generalized Laplace transform L2n and the generalized Glasser transform G2n. Using this identity a Parseval-Goldstein type theorem for the L2n-transform and the G2n-transform is given. By making use of these results a number of new Parseval-Goldstein type identities are obtained for these and many other well-known integral transforms. The identities proven in this paper are shown to give rise to useful corollaries for evaluating infinite integrals of special functions. Some examples are also given.

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39

Cho, Dong Hyun. "Integral Transforms on a Function Space with Change of Scales Using Multivariate Normal Distributions." Journal of Function Spaces 2016 (2016): 1–9. http://dx.doi.org/10.1155/2016/9235960.

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Using simple formulas for generalized conditional Wiener integrals on a function space which is an analogue of Wiener space, we evaluate two generalized analytic conditional Wiener integrals of a generalized cylinder function which is useful in Feynman integration theories and quantum mechanics. We then establish various integral transforms over continuous paths with change of scales for the generalized analytic conditional Wiener integrals. In these evaluation formulas and integral transforms we use multivariate normal distributions so that the orthonormalization process of projection vectors which are needed to establish the conditional Wiener integrals can be removed in the existing change of scale transforms. Consequently the transforms in the present paper can be expressed in terms of the generalized cylinder function itself.

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40

Sedeeg, Abdelilah Kamal H. "Some Properties and Applications of a New General Triple Integral Transform “Gamar Transform’’." Complexity 2023 (April 29, 2023): 1–21. http://dx.doi.org/10.1155/2023/5527095.

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The goal of this study is to suggest a new general triple integral transform known as Gamar transform. Next, we compare the current transform to a number of existing triple integral transforms such as those by Laplace, Sumudu, Elzaki, Aboodh, and Laplace–Aboodh–Sumudu. We outline its essential properties and prove some important results, including linearity property, existence theorem, triple convolution theorem, and derivatives properties. Moreover, the proposed new transform is applied to solve some partial differential equations (PDEs) such as Laplace, Mboctara, and Wave equations. The capacity of general triple integral transforms to change PDEs into simple algebraic equations is demonstrated.

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41

Bhoi, Jhasaketan, and Ujjwal Laha. "Integral Transforms and Their Applications to Scattering Theory." International Journal of Applied Physics and Mathematics 4, no. 6 (2014): 386–405. http://dx.doi.org/10.17706/ijapm.2014.4.6.386-405.

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42

Chung, Hyun Soo. "Generalized Integral Transforms via the Series Expressions." Mathematics 8, no. 4 (April 6, 2020): 539. http://dx.doi.org/10.3390/math8040539.

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From the change of variable formula on the Wiener space, we calculate various integral transforms for functionals on the Wiener space. However, not all functionals can be obtained by using this formula. In the process of calculating the integral transform introduced by Lee, this formula is also used, but it is also not possible to calculate for all the functionals. In this paper, we define a generalized integral transform. We then introduce a new method to evaluate the generalized integral transform for functionals using series expressions. Our method can be used to evaluate various functionals that cannot be calculated by conventional methods.

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43

Turq, Saed M., and Emad A. Kuffi. "Comparison of Complex Sadik and KAJ Transforms for Ordinary Differential Equations to the Response of an Uncompressed Forced Oscillator." Ibn AL-Haitham Journal For Pure and Applied Sciences 37, no. 1 (January 20, 2024): 442–53. http://dx.doi.org/10.30526/37.1.3326.

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In this paper we have presented a comparison between two novel integral transformations that are of great importance in the solution of differential equations. These two transformations are the complex Sadik transform and the KAJ transform. An uncompressed forced oscillator, which is an important application, served as the basis for comparison. The application was solved and exact solutions were obtained. Therefore, in this paper, the exact solution was found based on two different integral transforms: the first integral transform complex Sadik and the second integral transform KAJ. And these exact solutions obtained from these two integral transforms were new methods with simple algebraic calculations and applied to different problems. The main purpose of this comparison is the exact solutions, and until we show the importance of the diversity and difference of the kernel of the integral transform by keeping the period t between 0 and infinity.

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44

He, Ji-Huan, Naveed Anjumd, Chun-Hui Hee, and Abdulrahman Alsolamif. "Beyond Laplace and Fourier transforms: Challenges and future prospects." Thermal Science, no. 00 (2023): 224. http://dx.doi.org/10.2298/tsci230804224h.

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Laplace and Fourier transforms are widely used independently in engineering for linear differential equations including fractional differential equations. Here we introduce a generalized integral transform, which is a generalization of the Fourier transform, Laplace transform and other transforms, e.g., Elzaki Sumudu transform, Aboodh transform, Pourreza transform and Mohand transform, making the new transform much attractive and promising. Its basic properties are elucidated, and its applications to initial value problems and integral equations are illustrated, when coupled with the homotopy perturbation, it can be used for various nonlinear problems, opening a new window for nonlinear science.

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Aghili, Arman. "New trends in Laplace type integral transforms with applications." Boletim da Sociedade Paranaense de Matemática 35, no. 1 (October 26, 2017): 173. http://dx.doi.org/10.5269/bspm.v35i1.28645.

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AbstractIn this paper, the authors provided a discussion on one and two dimensional Laplace transforms and generalized Stieltjes transform and their applications in evaluating special series and integrals. Finally, we implemented the joint Laplace – Fourier transforms to construct exact solution for a variant of the Kd.V equation. Illustrative examples are also provided.

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Hwang, Gyeongha, and Sunghwan Moon. "Inversion formulas for quarter-spherical Radon transforms." AIMS Mathematics 8, no. 12 (2023): 31258–67. http://dx.doi.org/10.3934/math.20231600.

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<abstract><p>The applications of spherical Radon transforms include synthetic aperture radar, sonar tomography, and medical imaging modalities. A spherical Radon transform maps a function to its integrals over a family of spheres. Recently, several types of incomplete spherical Radon transforms have received attention in research. This study examines two types of quarter-spherical Radon transforms that assign a function to its integral over a quarter of a sphere: 1) center of a quarter sphere of integration on a plane, and 2) center on a line and the rotation of the quarter sphere. Furthermore, we present inversion formulas for these two quarter-spherical Radon transforms.</p></abstract>

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Attaweel, Mohamed E., and Haneen Almassry. "On the Mohand Transform and Ordinary Differential Equations with Variable Coefficients." Al-Mukhtar Journal of Sciences 35, no. 1 (January 30, 2020): 01–06. http://dx.doi.org/10.54172/mjsc.v35i1.229.

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The Mohand transform is a new integral transform introduced by Mohand M. Abdelrahim Mahgoub to facilitate the solution of differential and integral equations. In this article, a new integral transform, namely Mohand transform was applied to solve ordinary differential equations with variable coefficients by using the modified version of Laplace and Sumudu transforms.

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Musta (Xhaferraj), Ervenila. "The Complex Form of “NE” Integral Transform." All Sciences Abstracts 1, no. 1 (May 10, 2023): 10. http://dx.doi.org/10.59287/as-abstracts.652.

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In this paper, we present and construct a novel complex transform namely “Complex NE Transform”. The propositions of this transformation are investigated. The complex transform is used to convert the core problem to a simple algebraic equation. The definition and application of novel complex transforms to solve ordinary differential equations have been demonstrated.

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Britvina, L. E. "GENERAL CONVOLUTIONS OF INTEGRAL TRANSFORMS AND THEIR APPLICATION TO ODE AND PDE PROBLEMS." Mathematical Modelling and Analysis 11, no. 1 (March 31, 2006): 23–34. http://dx.doi.org/10.3846/13926292.2006.9637299.

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The present research is devoted to some polyconvolutions generated by various integral transforms. For example, we study convolutions of the Hankel transform with the following factorization properties: where Hv[f] (x) is the Hankel transform. Conditions for the existence of the constructed polyconvolutions are found. The results of this research are applied for solvability of ODEs and PDEs by the method of integral transforms. The derived constructions allow us to solve various nonuniform equations.

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Kim, Hwajoon. "The Intrinsic Structure and Properties of Laplace-Typed Integral Transforms." Mathematical Problems in Engineering 2017 (2017): 1–8. http://dx.doi.org/10.1155/2017/1762729.

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We would like to establish the intrinsic structure and properties of Laplace-typed integral transforms. The methodology of this article is done by a consideration with respect to the common structure of kernels of Laplace-typed integral transform, and G-transform, the generalized Laplace-typed integral transform, is proposed with the feature of inclusiveness. The proposed G-transform can provide an adequate transform in a number of engineering problems.

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