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Journal articles on the topic 'Integral transforms'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

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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2

Aghili, Arman. "Non-homogeneous impulsive time fractional heat conduction equation." Journal of Numerical Analysis and Approximation Theory 52, no. 1 (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 math

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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 (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

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4

Salamat, Kaushef, and Nousheen Ilyas. "DUALITIES BETWEEN FOURIER SINE AND SOME USEFUL INTEGRAL TRANSFORMATIONS." Journal of Mathematical Sciences & Computational Mathematics 2, no. 4 (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 me

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Luchko, Yuri. "Some Schemata for Applications of the Integral Transforms of Mathematical Physics." Mathematics 7, no. 3 (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-

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6

Iyeme, E. E., and O. R. Okpo. "Introduction of New General Laplace-Type Integral Transform: The Iyeme-Okpo Transform." Journal of Applied Sciences and Environmental Management 29, no. 3 (2025): 725–28. https://doi.org/10.4314/jasem.v29i3.5.

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In this paper, a new general Laplace-type integral transform called Iyeme-Okpo transform that generalizes all the existing Laplace-type integral transforms has been introduced. Thus, existing integral transforms such as Laplace, Sumudu, Natural, Jafari, Elzaki, Mahgoub, Kamal, Mohand, Sawi, Aboodh, HY, Anuj, Y, Soham, G, Kushare, Emad-Falih, ZZ, SEE, Iman, R, and Formable transforms are special cases of this general transform. Also, we can introduce new Laplace-type integral transforms using this general transform.

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KABRA, SEEMA, and HARISH NAGAR. "INTEGRAL TRANSFORM OF K4-FUNCTION." Journal of Science and Arts 21, no. 2 (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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8

Gwila, Nbila, and Ali Farhat. "GF1 Integral Transform and its Some Applications." مجلة الجامعة الأسمرية: العلوم التطبيقية 7, no. 2 (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 i

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9

Mlaiki, Nabil, Noor Jamal, Muhammad Sarwar, Manel Hleili, and Khursheed J. Ansari. "Duality of Shehu transform with other well known transforms and application to fractional order differential equations." PLOS One 20, no. 4 (2025): e0318157. https://doi.org/10.1371/journal.pone.0318157.

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Integral transforms are used in many research articles in the literature, due to their interesting applications in the solutions of problems of applied science and engineering. In many situations, researchers feel difficulties in applying a given transform to solve differential or integral equations, therefore it is more convenient to derive dualities relations between these transforms. Shehu transform has the properties to converge to the well-known integral transforms used in the literature only by changing the space parameters. In this article, we will derive the inter-conversion relations

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10

ZORICH, Anton. "INVERSION OF HOROSPHERICAL INTEGRAL TRANSFORM ON REAL SEMISIMPLE LIE GROUPS." International Journal of Modern Physics A 07, supp01b (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. N

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11

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 (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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12

Man'ko, Margarita A. "Propagators, Tomograms, Wavelets and Quasidistributions for Multipartite Quantum Systems." Open Systems & Information Dynamics 14, no. 02 (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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13

Campos, Harren, Jezer Fernandez, and Jade Bong Natuil. "On Degenerate Laplace-type Integral Transform." European Journal of Pure and Applied Mathematics 16, no. 4 (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

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14

Jagtap, R. R., P. G. Andhare та S. B. Gaikwad. "A New General Integral Transform of Modified Laguerre’s Polynomial 𝐿𝐚,𝐛,𝐜,𝐧(𝑡)". Indian Journal Of Science And Technology 17, № 39 (2024): 4066–72. http://dx.doi.org/10.17485/ijst/v17i39.1251.

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Objectives: The core objective of this paper is to introduce the explicit Modified Laguerre polynomial 𝐿𝑎,𝑏,𝑐,𝑛 (𝑡) and obtain a new general integral transform of Modified Laguerre’s Polynomial, by using this general transform, some transforms of Laguerre’s Polynomial are identified as special cases. Method: We derive transforms of the polynomials 𝐿𝑎,𝑏,𝑐,𝑛 (𝑡), 𝐿𝑛 (𝑡) by using this new integral transform approach and found the transforms like Laplace, 𝛼-Laplace, Sawi, Elzaki, Sumudu, Natural, Aboodh, Pourreza, Mohand, G_transform, Kamal transforms and their relationship for the same. Findings:

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15

Bhandari, Piyush Kumar, and Sushil Kumar Bissu. "Inequalities for some classical integral transforms." Tamkang Journal of Mathematics 47, no. 3 (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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16

Khan, Sana Ullah, Asif Khan, Aman Ullah, et al. "Solving nth-order Integro-differential Equations by Novel Generalized Hybrid Transform." European Journal of Pure and Applied Mathematics 16, no. 3 (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,

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17

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

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18

D'Costa, Liya, and Naresh Menaria. "New Integral Transforms of the Extended k- Generalized Mittag-Leffler Function with Graphical Representations." European Journal of Pure and Applied Mathematics 17, no. 4 (2024): 4164–79. http://dx.doi.org/10.29020/nybg.ejpam.v17i4.5557.

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Different integral transforms have extensive applications in the various areas of science and engineering. Some of the new integral transforms of extended k-generalized Mittag-Leffler function are discussed in this paper. We examine integral transforms such as the Euler-Beta, Laplace, Mohand, Aboodh, SEE, and Sadik transform. Moreover, we also tried to establish the graphical representations of these transforms.

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19

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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20

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 (2018): 345–49. http://dx.doi.org/10.14445/22315373/ijmtt-v55p545.

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21

Xhaferraj, Ervenila Musta. "The New Integral Transform: “NE Transform” and Its Applications." European Journal of Formal Sciences and Engineering 6, no. 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 us

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22

Rodrigo, Marianito R., and Mandy Li. "Analogues of the Laplace Transform and Z-Transform with Piecewise Linear Kernels." Foundations 1, no. 1 (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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23

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

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24

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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25

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

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26

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 (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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27

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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28

R, R. Jagtap, G. Andhare P та B. Gaikwad S. "A New General Integral Transform of Modified Laguerre's Polynomial 𝐿𝐚,𝐛,𝐜,𝐧(𝑡)". Indian Journal of Science and Technology 17, № 39 (2024): 4066–72. https://doi.org/10.17485/IJST/v17i39.1251.

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Abstract <strong>Objectives:</strong> The core objective of this paper is to introduce the explicit Modified Laguerre polynomial 𝐿𝑎,𝑏,𝑐,𝑛 (𝑡) and obtain a new general integral transform of Modified Laguerre’s Polynomial, by using this general transform, some transforms of Laguerre’s Polynomial are identified as special cases. <strong>Method:</strong> We derive transforms of the polynomials 𝐿𝑎,𝑏,𝑐,𝑛 (𝑡), 𝐿𝑛 (𝑡) by using this new integral transform approach and found the transforms like Laplace, 𝛼-Laplace, Sawi, Elzaki, Sumudu, Natural, Aboodh, Pourreza, Mohand, G_tran

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29

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 (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

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30

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

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31

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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32

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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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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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 obt

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35

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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36

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 Sheh

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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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38

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

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39

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 (2017): 1–8. http://dx.doi.org/10.9734/bjast/2017/32380.

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40

BATOOL, SAIMA, GHULAM FARID, and SADIA KOUSAR. "SOME INTEGRAL TRANSFORMS INVOLVING GENERALIZED BESSEL-MAITLAND FUNCTION." Journal of Science and Arts 23, no. 3 (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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N. O., Onuoha. "Kamal Transform of Unit Step Functions." African Journal of Mathematics and Statistics Studies 7, no. 3 (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 s

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42

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

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43

Negrín, Emilio R., Jeetendrasingh Maan, and Benito J. González. "Mellin and Widder–Lambert Transforms with Applications in the Salem Equivalence to the Riemann Hypothesis." Axioms 14, no. 2 (2025): 129. https://doi.org/10.3390/axioms14020129.

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This paper presents a comprehensive study of Plancherel’s theorem and inversion formulae for the Widder–Lambert transform, extending its scope to Lebesgue integrable functions, compactly supported distributions, and regular distributions with compact support. By employing the Plancherel theorem for the classical Mellin transform, we derive a corresponding Plancherel’s theorem specific to the Widder–Lambert transform. This novel approach highlights an intriguing connection between these integral transforms, offering new insights into their role in harmonic analysis. Additionally, we explore a c

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Ricci, P. E., and G. Mastroianni. "ERROR ESTIMATES FOR A CLASS OF INTEGRAL AND DISCRETE TRANSFORMS." Studia Scientiarum Mathematicarum Hungarica 36, no. 3-4 (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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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 capa

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Dinkar, P. Patil, D. Thakare Prerana, and R. Patil Prajakta. "General Integral Transform for the Solution of Models in Health Sciences." International Journal of Innovative Science and Research Technology 7, no. 12 (2023): 1177–83. https://doi.org/10.5281/zenodo.7511243.

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Recently many researchers introduced lot of integral transforms. Integral transforms play important role for solving differential equations, integral equations, Integro differential equations, difference equations and systems. General integral transform is introduced by Hossein Jafari in 2021. We have models in health sciences which contains a system of differential equations with boundary conditions. In this paper we solve two models. First model is, two compartment model for drug absorption and circulation through gastrointestinal tract and blood. Second model is, Model for the intravenous d

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Khurshid, Shaheela, and Nnadozie Shahnaz. "Mohand Transformation of Solutions to Integral Equations and Abel Equations." Journal of Research in Vocational Education 6, no. 7 (2024): 1–4. http://dx.doi.org/10.53469/jrve.2024.06(07).01.

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Integral transforms play a crucial role in determining the precise solution to differential equations and are distinguished by their simplicity and convenience. Several academics, beginning with Laplace, have formulated comprehensive equations for integral transforms. These transformations also hold significant importance in discovering precise answers to physical, technical, medicinal, and nuclear challenges, as well as in the fields of astronomy and economics. There are various types of integral transforms like Elzaki, Kamal, Aboodh, Mahgoub, sawi, Rishi, Anuj, Tarig, Kushare, Upadhyaya etc.

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Savita, Santu Khakale, Sahadu Ahire Kailas, and Pitambar Patil Dinkar. "Soham Transform in Fractional Differential Equations." Indian Journal of Science and Technology 17, no. 33 (2024): 3481–87. https://doi.org/10.17485/IJST/v17i33.1383.

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Abstract <strong>Objectives:</strong> Soham transforms is one of the appropriate tools for solving fractional differential equations that are flexible enough to adapt to different purposes. <strong>Methods:</strong> Integral transform methods help to simplify fractional differential equations into algebraic equations. Enable the use of classical methods to solve fractional differential equations. <strong>Findings:</strong> In this paper, the Soham transform can solve linear homogeneous and non-homogeneous Fractional Differential Equations with constant coefficients. Fi

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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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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 (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

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