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Journal articles on the topic 'Double Laplace – Upadhyaya Transform'

Author: Grafiati

Published: 5 June 2025

Last updated: 2 August 2025

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1

Al-Momani, Monther, Ali Jaradat, and Baha Abughazale. "Double Laplace-Sawi Transform." European Journal of Pure and Applied Mathematics 18, no. 1 (2025): 5619. https://doi.org/10.29020/nybg.ejpam.v18i1.5619.

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The primary objective of this study is to develop a new integral transform by combining the Laplace and Sawi transforms, and to investigate its key properties, existence, and the inversion theorem. Furthermore, we introduce new results related to partial differential equations in higher dimensions and extend the double convolution theorem to two dimensions. Using these new properties and theorems, we solve special type differential equations with some real applications in physics and related sciences.

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2

Ranjit, Dhunde, and Dhongle Prashant. "Solving Two-Dimensional Helmholtz and Poisson Equations Using Double Laplace Transform Method." Indian Journal of Science and Technology 18, no. 12 (2025): 962–68. https://doi.org/10.17485/IJST/v18i12.3705.

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Abstract <strong>Objectives:</strong> To explore the efficacy of the double Laplace transform technique in solving 2D Helmholtz and Poisson equations. <strong>Methods:</strong> The double Laplace transform clearly converts the 2D Helmholtz and Poisson equations into an algebraic calculation in the Laplace domain that can be solved easily. <strong>Findings:</strong> The double Laplace transform method offers exact solutions to the Helmholtz and Poisson equations by resolving a series of specific and understandable examples. <strong>Novelty:</strong> This resea

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3

Eltayeb, Hassan, and Said Mesloub. "The New G-Double-Laplace Transforms and One-Dimensional Coupled Sine-Gordon Equations." Axioms 13, no. 6 (2024): 385. http://dx.doi.org/10.3390/axioms13060385.

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This paper establishes a novel technique, which is called the G-double-Laplace transform. This technique is an extension of the generalized Laplace transform. We study its properties with examples and various theorems related to the G-double-Laplace transform that have been addressed and proven. Finally, we apply the G-double-Laplace transform decomposition method to solve the nonlinear sine-Gordon and coupled sine-Gordon equations. This method is a combination of the G-double-Laplace transform and decomposition method. In addition, some examples are examined to establish the accuracy and effe

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4

Shabestari, R. Mastani, and R. Ezzati. "The Fuzzy Double Laplace Transforms and their Properties with Applications to Fuzzy Wave Equation." New Mathematics and Natural Computation 17, no. 02 (2021): 319–38. http://dx.doi.org/10.1142/s1793005721500174.

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The main focus of this paper is develop of the fuzzy double Laplace transform to solve a fuzzy wave equation. In this scheme, a fuzzy wave equation can be solved without converting it to two crisp equations. Some properties of the fuzzy Laplace transform and the fuzzy double Laplace transform are proved. The superiority and accuracy of the fuzzy double Laplace transform to wave equation are illustrated through some examples.

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5

Eltayeb, Hassan. "Note on Relation between Double Laplace Transform and Double Differential Transform." Abstract and Applied Analysis 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/535020.

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6

Dhunde, Ranjit R. "Double Laplace Transform Method for Solving Fractional Fourth-Order Partial Integro-Differential Equations with Weakly Singular Kernel." Indian Journal Of Science And Technology 17, no. 36 (2024): 3712–18. http://dx.doi.org/10.17485/ijst/v17i36.2005.

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Objectives: To investigates the solutions of fourth order partial integro-differential equations with high-order non-integer derivatives and weakly singular kernels. Methods: Weakly singular kernels present challenges in both analytical and numerical treatments due to their intricate behaviour near singular points. In this article, we introduce a novel approach utilizing the double Laplace transform method to effectively address these challenges. Findings: By solving a series of precise and understandable examples, the double Laplace transform clearly transforms the fractional partial integro-

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7

Ahmed, Shams A. "Applications of New Double Integral Transform (Laplace–Sumudu Transform) in Mathematical Physics." Abstract and Applied Analysis 2021 (March 1, 2021): 1–8. http://dx.doi.org/10.1155/2021/6625247.

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The primary purpose of this research is to demonstrate an efficient replacement of double transform called the double Laplace–Sumudu transform (DLST) and prove some related theorems of the new double transform. Also, we will discuss the fundamental properties of the double Laplace–Sumudu transform of some basic functions. Then, by utilizing those outcomes, we will apply it to the partial differential equations to show its simplicity, efficiency, and high accuracy.

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8

Kiliçman, A., and H. E. Gadain. "An application of double Laplace transform and double Sumudu transform." Lobachevskii Journal of Mathematics 30, no. 3 (2009): 214–23. http://dx.doi.org/10.1134/s1995080209030044.

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9

Ranjit, R. Dhunde. "Double Laplace Transform Method for Solving Fractional Fourth-Order Partial Integro-Differential Equations with Weakly Singular Kernel." Indian Journal of Science and Technology 17, no. 36 (2024): 3712–18. https://doi.org/10.17485/IJST/v17i36.2005.

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Abstract <strong>Objectives:</strong> To investigates the solutions of fourth order partial integro-differential equations with high-order non-integer derivatives and weakly singular kernels. <strong>Methods:</strong> Weakly singular kernels present challenges in both analytical and numerical treatments due to their intricate behaviour near singular points. In this article, we introduce a novel approach utilizing the double Laplace transform method to effectively address these challenges. <strong>Findings:</strong> By solving a series of precise and understandable exam

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10

Borawake, Vijay, and Anil Hiwarekar. "Modified double Laplace transform of partial derivatives and its applications." Gulf Journal of Mathematics 16, no. 2 (2024): 353–63. http://dx.doi.org/10.56947/gjom.v16i2.1892.

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This paper deals with modified double Laplace transforms of partial derivatives and their applications. Starting with standard results on modified double Laplace transform, we developed theorems on modified double Laplace transform of first and second-order partial derivatives. Further, we applied our results to solve homogeneous and non-homogeneous partial differential equations, D' Alembert's wave equation, and Klein-Gordon equation.

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11

Sedeeg, Abdelilah Kamal, Zahra I. Mahamoud, and Rania Saadeh. "Using Double Integral Transform (Laplace-ARA Transform) in Solving Partial Differential Equations." Symmetry 14, no. 11 (2022): 2418. http://dx.doi.org/10.3390/sym14112418.

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The main goal of this research is to present a new approach to double transforms called the double Laplace–ARA transform (DL-ARAT). This new double transform is a novel combination of Laplace and ARA transforms. We present the basic properties of the new approach including existence, linearity and some results related to partial derivatives and the double convolution theorem. To obtain exact solutions, the new double transform is applied to several partial differential equations such as the Klein–Gordon equation, heat equation, wave equation and telegraph equation; each of these equations has

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12

Honggang, Jia, and Zhao Yanmin. "Conformable Double Laplace–Sumudu Transform Decomposition Method for Fractional Partial Differential Equations." Complexity 2022 (August 25, 2022): 1–8. http://dx.doi.org/10.1155/2022/7602254.

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In this work, we proposed a new method called conformable fractional double Laplace–Sumudu transform decomposition method (CFDLSTDM) to solve fractional partial differential equations (FPDEs).This method is a combination of the Laplace–Sumudu transform method and the Adomian decomposition method. Besides, we presented some excellent properties and results of conformable double Laplace–Sumudu transform (CDLST). Illustrative examples results are given to show that the CFDLSTDM is an effective and accurate approach for fractional partial differential equations.

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13

Pavlov, Andrey. "The Regularity of the Laplace Transform." Mathematical Physics and Computer Simulation, no. 1 (April 2019): 5–11. http://dx.doi.org/10.15688/mpcm.jvolsu.2019.1.1.

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The paper proves the regularity of the double Laplace transform in the neighborhood of zero. The class of the transform of Laplace from the transform of Fourier is considered from the functions without a regularity in null.

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14

Poltem, Duangkamol, and Araya Wiwatwanich. "A New Double Integral Transform for Solving Partial Integro-Differential Equation." International Journal of Mathematics and Computer Science 20, no. 1 (2024): 79–88. http://dx.doi.org/10.69793/ijmcs/01.2025/wiwatwanich.

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In this paper, we propose a new double integral transform operator, called the Laplace-General transform. Moreover, we establish several basic properties and fundamental theorems of the Laplace-General transform. Furthermore, we apply the theoretical results to a class of partial integro-differential equations as an illustrative example.

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15

GadAllah, Musa Rahamh, and Hassan Eltayeb Gadain. "Conformable Double Laplace Transform Method (CDLTM) and Homotopy Perturbation Method (HPM) for Solving Conformable Fractional Partial Differential Equations." Symmetry 16, no. 9 (2024): 1232. http://dx.doi.org/10.3390/sym16091232.

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In the present article, the method which was obtained from a combination of the conformable fractional double Laplace transform method (CFDLTM) and the homotopy perturbation method (HPM) was successfully applied to solve linear and nonlinear conformable fractional partial differential equations (CFPDEs). We included three examples to help our presented technique. Moreover, the results show that the proposed method is efficient, dependable, and easy to use for certain problems in PDEs compared with existing methods. The solution graphs show close contact between the exact and CFDLTM solutions.

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16

Łochowski, Rafał Marcin. "On the double Laplace transform of the truncated variation of a Brownian motion with drift." LMS Journal of Computation and Mathematics 19, no. 1 (2016): 281–92. http://dx.doi.org/10.1112/s1461157016000127.

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The aim of this paper is to find a formula for the double Laplace transform of the truncated variation of a Brownian motion with drift. In order to find the double Laplace transform, we also prove some identities for the Brownian motion with drift, which may be of independent interest.

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17

Gadain, Hassan. "Nonlinear singular one dimensional thermo-elasticity coupled system and double Laplace decomposition methods." Filomat 31, no. 20 (2017): 6269–80. http://dx.doi.org/10.2298/fil1720269g.

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In this work, combined double Laplace transform and Adomian decomposition method is presented to solve nonlinear singular one dimensional thermo-elasticity coupled system. Moreover, the convergence proof of the double Laplace transform decomposition method applied to our problem. By using one example, our proposed method is illustrated and the obtained results are confirmed.

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18

Ahmed, Shams A., Tarig M. Elzaki, and Abdelgabar Adam Hassan. "Solution of Integral Differential Equations by New Double Integral Transform (Laplace–Sumudu Transform)." Abstract and Applied Analysis 2020 (October 18, 2020): 1–7. http://dx.doi.org/10.1155/2020/4725150.

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The primary purpose of this research is to demonstrate an efficient replacement double transform named the Laplace–Sumudu transform (DLST) to unravel integral differential equations. The theorems handling fashionable properties of the Laplace–Sumudu transform are proved; the convolution theorem with an evidence is mentioned; then, via the usage of these outcomes, the solution of integral differential equations is built.

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19

Abu Awwad, Raed, Monther Al-Momani, Baha' Abughazaleh, Ali Jaradat, and Abdulkarim Farah. "The Conformable DoubleLaplace-Sawi Transform." European Journal of Pure and Applied Mathematics 18, no. 2 (2025): 6034. https://doi.org/10.29020/nybg.ejpam.v18i2.6034.

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In this study, we introduce the conformable double Laplace-Sawi transform, a method for solving fractional partial differential equations that appear in various physical and engineering models. These models use derivatives and integrals based on the newly defined conformable derivative. The study first explores key properties of the conformable double Laplace-Sawi transform. Then, as an application, the method is applied to solving the conformable telegraph equation, the conformable heat equation, and the conformable Klein-Gordon equation, which are widely used in scientific and engineering fi

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20

Eltayeb, Hassan, Imed Bachar, and Adem Kılıçman. "On Conformable Double Laplace Transform and One Dimensional Fractional Coupled Burgers’ Equation." Symmetry 11, no. 3 (2019): 417. http://dx.doi.org/10.3390/sym11030417.

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In the present work we introduced a new method and name it the conformable double Laplace decomposition method to solve one dimensional regular and singular conformable functional Burger’s equation. We studied the existence condition for the conformable double Laplace transform. In order to obtain the exact solution for nonlinear fractional problems, then we modified the double Laplace transform and combined it with the Adomian decomposition method. Later, we applied the new method to solve regular and singular conformable fractional coupled Burgers’ equations. Further, in order to illustrate

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21

Eltayeb, Hassan, Adem Kılıçman, and Brian Fisher. "On Multiple Convolutions and Time Scales." Mathematical Problems in Engineering 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/217656.

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The properties of the multiple Laplace transform and convolutions on a time scale are studied. Further, some related results are also obtained by utilizing the double Laplace transform. We also provide an example in order to illustrate the main result.

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22

Maryam, Omran. "A Note on Fractional Double Natural Transform." AlQalam Journal of Medical and Applied Sciences 4, no. 1 (2021): 85–90. https://doi.org/10.5281/zenodo.4442629.

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In this article, we present a definition of fractional double Natural transform of order α, 0<α≤1, for fractional differentiable functions.  Some essential properties of fractional double Natural transform are determined. Furthermore, we set a relation between fractional double Natural transform and fractional double Laplace, fractional double Sumudu transforms.

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23

Haider, Syed Sabyel, Mujeeb Ur Rehman, and Thabet Abdeljawad. "A Transformation Method for Delta Partial Difference Equations on Discrete Time Scale." Mathematical Problems in Engineering 2020 (July 10, 2020): 1–14. http://dx.doi.org/10.1155/2020/3902931.

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The aim of this study is to develop a transform method for discrete calculus. We define the double Laplace transforms in a discrete setting and discuss its existence and uniqueness with some of its important properties. The delta double Laplace transforms have been presented for integer and noninteger order partial differences. For illustration, the delta double Laplace transforms are applied to solve partial difference equation.

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24

Qazza, Ahmad. "Solution of Integral Equations via Laplace ARA Transform." European Journal of Pure and Applied Mathematics 16, no. 2 (2023): 919–33. http://dx.doi.org/10.29020/nybg.ejpam.v16i2.4745.

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This research article demonstrates an efficient method for solving partial integro-differential equations. The intention of this research is to establish the solution of some different classes of integral equations, by utilizing the double Laplace ARA transform. We present some definitions and basic concepts related to the double Laplace ARA transform. The results of the examples support the theoretical results and show the accuracy and applicability of the presented approach.

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25

Eltayeb, Hassan. "Application of the Double Sumudu-Generalized Laplace Transform Decomposition Method to Solve Singular Pseudo-Hyperbolic Equations." Symmetry 15, no. 9 (2023): 1706. http://dx.doi.org/10.3390/sym15091706.

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In this study, the technique established by the double Sumudu transform in combination with a new generalized Laplace transform decomposition method, which is called the double Sumudu-generalized Laplace transform decomposition method, is applied to solve general two-dimensional singular pseudo-hyperbolic equations subject to the initial conditions. The applicability of the proposed method is analyzed through demonstrative examples. The results obtained show that the procedure is easy to carry out and precise when employed for different linear and non-linear partial differential equations.

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26

Pardeshi, Yuvraj. "Analytical Solution of Partial Integro Differential Equations Using Laplace Differential Transform Method and Comparison with DLT and DET." Asian Journal of Applied Science and Technology 06, no. 02 (2022): 127–37. http://dx.doi.org/10.38177/ajast.2022.6214.

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Partial Integro Differential Equations (PIDEs) occur naturally in various fields of science and technology. The main purpose of this paper is to study how to solve linear partial integro differential equations with convolution kernel by using the Laplace-Differential Transform Method (LDTM). This method is a simple and reliable technique for solving such equations. The efficiency and reliability of this method is also illustrated with some examples. The result obtained by this method is compared with the result obtained by Double Laplace Transform and Double Elzaki Transform method.

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27

Zhang, Wei. "Double Laplace Transform Computing Dynamic Response of the Large Thickness to Span Ratio Beam." Advanced Materials Research 834-836 (October 2013): 1333–36. http://dx.doi.org/10.4028/www.scientific.net/amr.834-836.1333.

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In this paper, use double Laplace transform, in the image space deep beam deflection and corner of analytic is obtained,Then use the numerical inversion of Laplace transform ,time domain dynamic response curve is calculated. Also apply to the combined effects of sandwich beam bending and torsion beam dynamic response calculation.

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28

Abrori, Muchammad, Sugiyanto, and Hana Mei Satriana Sari. "DOUBLE LAPLACE TRANSFORM METHOD FOR SOLVING TELEGRAPH EQUATION." JP Journal of Heat and Mass Transfer 17, no. 1 (2019): 265–75. http://dx.doi.org/10.17654/hm017010265.

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29

Talukdar, B., U. Laha, and S. R. Bhattaru. "Double Laplace transform of the Coulomb Green function." Journal of Physics A: Mathematical and General 18, no. 7 (1985): L359—L361. http://dx.doi.org/10.1088/0305-4470/18/7/005.

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30

Khan, T. G. Thange, and Sneha Chhatraband. "LAPLACE-SUMUDU INTEGRAL TRANSFORM ON TIME SCALES." South East Asian J. of Mathematics and Mathematical Sciences 19, no. 01 (2023): 91–102. http://dx.doi.org/10.56827/seajmms.2023.1901.9.

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31

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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32

Eltayeb, Hassan, and Adem Kiliçman. "A Note on Double Laplace Transform and Telegraphic Equations." Abstract and Applied Analysis 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/932578.

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Double Laplace transform is applied to solve general linear telegraph and partial integrodifferential equations. The scheme is tested through some examples, and the results demonstrate reliability and efficiency of the proposed method.

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33

Janson, Svante, and Niclas Petersson. "The Integral of the Supremum Process of Brownian Motion." Journal of Applied Probability 46, no. 2 (2009): 593–600. http://dx.doi.org/10.1239/jap/1245676109.

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In this paper we study the integral of the supremum process of standard Brownian motion. We present an explicit formula for the moments of the integral (or area)(T) covered by the process in the time interval [0,T]. The Laplace transform of(T) follows as a consequence. The main proof involves a double Laplace transform of(T) and is based on excursion theory and local time for Brownian motion.

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Janson, Svante, and Niclas Petersson. "The Integral of the Supremum Process of Brownian Motion." Journal of Applied Probability 46, no. 02 (2009): 593–600. http://dx.doi.org/10.1017/s0021900200005672.

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In this paper we study the integral of the supremum process of standard Brownian motion. We present an explicit formula for the moments of the integral (or area)(T) covered by the process in the time interval [0,T]. The Laplace transform of(T) follows as a consequence. The main proof involves a double Laplace transform of(T) and is based on excursion theory and local time for Brownian motion.

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35

Dhunde, Ranjit R. "Applications of Double Laplace Transform to Boundary Value Problems." IOSR Journal of Mathematics 9, no. 2 (2013): 57–60. http://dx.doi.org/10.9790/5728-0925760.

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36

D.O., Anongo, and Awari Y.S. "Solution of One-dimensional Partial Differential Equation with Higher-Order Derivative by Double Laplace Transform Method." African Journal of Mathematics and Statistics Studies 4, no. 3 (2021): 1–11. http://dx.doi.org/10.52589/ajmss-1ohgjpnr.

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Many problems in natural and engineering sciences such as heat transfer, elasticity, quantum mechanics, water flow, and others are modelled mathematically by partial differential equations. Some of these problems may be linear, nonlinear, homogeneous, non-homogeneous, and order greater or equal one. Finding the theoretical solution to these problems with less cumbersome techniques is an active area of research in the aforementioned field. In this research paper, we have developed a new application of the double Laplace transform method to solve homogeneous and non-homogeneous linear partial di

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Dassios, Angelos, and Shanle Wu. "Double-Barrier Parisian Options." Journal of Applied Probability 48, no. 1 (2011): 1–20. http://dx.doi.org/10.1239/jap/1300198132.

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In this paper we study the excursion time of a Brownian motion with drift outside a corridor by using a four-state semi-Markov model. In mathematical finance, these results have an important application in the valuation of double-barrier Parisian options. We subsequently obtain an explicit expression for the Laplace transform of its price.

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Dassios, Angelos, and Shanle Wu. "Double-Barrier Parisian Options." Journal of Applied Probability 48, no. 01 (2011): 1–20. http://dx.doi.org/10.1017/s0021900200007592.

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In this paper we study the excursion time of a Brownian motion with drift outside a corridor by using a four-state semi-Markov model. In mathematical finance, these results have an important application in the valuation of double-barrier Parisian options. We subsequently obtain an explicit expression for the Laplace transform of its price.

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Eltayeb, Hassan, Adem Kılıçman, and Said Mesloub. "Exact Evaluation of Infinite Series Using Double Laplace Transform Technique." Abstract and Applied Analysis 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/327429.

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Double Laplace transform method was applied to evaluate the exact value of double infinite series. Further we generalize the current existing methods and provide some examples to illustrate and verify that the present method is a more general technique.

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Ahmed, Shams A., Ahmad Qazza, Rania Saadeh, and Tarig M. Elzaki. "Conformable Double Laplace–Sumudu Iterative Method." Symmetry 15, no. 1 (2022): 78. http://dx.doi.org/10.3390/sym15010078.

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This research introduces a novel approach that combines the conformable double Laplace–Sumudu transform (CDLST) and the iterative method to handle nonlinear partial problems considering some given conditions, and we call this new approach the conformable Laplace–Sumudu iterative (CDLSI) method. Furthermore, we state and discuss the main properties and the basic results related to the proposed technique. The new method provides approximate series solutions that converge to a closed form of the exact solution. The advantage of using this method is that it produces analytical series solutions for

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41

Issa, Ahmad, and Emad A. Kuffi. "On The Double Integral Transform (Complex EE Transform) and Their Properties and Applications." Ibn AL-Haitham Journal For Pure and Applied Sciences 37, no. 1 (2024): 429–41. http://dx.doi.org/10.30526/37.1.3329.

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Due to the importance of solutions of partial differential equations, linear, nonlinear, homogeneous, and non-homogeneous, in important life applications, including engineering applications, physics and astronomy, medical sciences, and life technology, and their importance in solutions to heat transfer equations, wave, Laplace equation, telegraph, etc. In this paper, a new double integral transform has been proposed. In this work, we have introduced a new double transform ( Double Complex EE Transform ). In addition, we presented the convolution theorem and proved the properties of the propose

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Eltayeb, Hassan, and Said Mesloub. "Solution for Time-Fractional Coupled Burgers Equations by Generalized-Laplace Transform Methods." Fractal and Fractional 8, no. 12 (2024): 692. http://dx.doi.org/10.3390/fractalfract8120692.

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In this work, nonlinear time-fractional coupled Burgers equations are solved utilizing a computational method, which is called the double and triple generalized-Laplace transform and decomposition method. We discuss the proof of triple generalized-Laplace transform for a Caputo fractional derivative. We have given four examples to show the precision and adequacy of the suggested approach. The results show that this method is easy and accurate when compared to the A domain decomposition method (ADM), homotopy perturbation method (HPM), and generalized differential transform method (GDTM). Final

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M. Turq, Saed, and Emad A. Kuffi. "On the Double of the Emad - Falih Transformation and Its Properties with Applications." Ibn AL-Haitham Journal For Pure and Applied Sciences 35, no. 4 (2022): 220–34. http://dx.doi.org/10.30526/35.4.2938.

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In this paper, we have generalized the concept of one dimensional Emad - Falih integral transform into two dimensional, namely, a double Emad - Falih integral transform. Further, some main properties and theorems related to the double Emad - Falih transform are established. To show the proposed transform's efficiency, high accuracy, and applicability, we have implemented the new integral transform for solving partial differential equations. Many researchers have used double integral transformations in solving partial differential equations and their applications. One of the most important uses

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Avram, F., and M. Usábel. "Ruin Probabilities and Deficit for the Renewal Risk Model with Phase-type Interarrival Times." ASTIN Bulletin 34, no. 02 (2004): 315–32. http://dx.doi.org/10.2143/ast.34.2.505146.

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This paper shows how the multivariate finite time ruin probability function, in a phase-type environment, inherits the phase-type structure and can be efficiently approximated with only one Laplace transform inversion. From a theoretical point of view, we also provide below a generalization of Thorin’s formula (1971) for the double Laplace transform of the finite time ruin probability, by considering also the deficit at ruin; the model is that of a Sparre Andersen (renewal) risk process with phase-type interarrival times. In the case when the claims distribution is of phase-type as well, we ob

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Avram, F., and M. Usábel. "Ruin Probabilities and Deficit for the Renewal Risk Model with Phase-type Interarrival Times." ASTIN Bulletin 34, no. 2 (2004): 315–32. http://dx.doi.org/10.1017/s0515036100013714.

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This paper shows how the multivariate finite time ruin probability function, in a phase-type environment, inherits the phase-type structure and can be efficiently approximated with only one Laplace transform inversion.From a theoretical point of view, we also provide below a generalization of Thorin’s formula (1971) for the double Laplace transform of the finite time ruin probability, by considering also the deficit at ruin; the model is that of a Sparre Andersen (renewal) risk process with phase-type interarrival times.In the case when the claims distribution is of phase-type as well, we obta

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Lemnaouar, M. R., and I. El Hakki. "On the double Laplace transform with respect to another function." Chaos, Solitons & Fractals 194 (May 2025): 116237. https://doi.org/10.1016/j.chaos.2025.116237.

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Jia, Honggang, Yufeng Nie, and Yanmin Zhao. "GENERAL CONFORMABLE FRACTIONAL DOUBLE LAPLACE-SUMUDU TRANSFORM AND ITS APPLICATION." Journal of Applied Analysis & Computation 15, no. 1 (2025): 9–20. https://doi.org/10.11948/20220344.

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Ohshima, Hiroyuki. "Approximate Analytic Expression for the Time-Dependent Transient Electrophoretic Mobility of a Spherical Colloidal Particle." Molecules 27, no. 16 (2022): 5108. http://dx.doi.org/10.3390/molecules27165108.

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Abstract:

The general expression is derived for the Laplace transform of the time-dependent transient electrophoretic mobility (with respect to time) of a spherical colloidal particle when a step electric field is applied. The transient electrophoretic mobility can be obtained by the numerical inverse Laplace transformation method. The obtained expression is applicable for arbitrary particle zeta potential and arbitrary thickness of the electrical double layer around the particle. For the low potential case, this expression gives the result obtained by Huang and Keh. On the basis of the obtained general

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Ziane, Djelloul, Mountassir Hamdi Cherif, Carlo Cattani, and Abdelhamid Mohammed Djaouti. "Double Local Fractional Yang–Laplace Transform for Local Fractional PDEs on Fractal Domains." Fractal and Fractional 9, no. 7 (2025): 434. https://doi.org/10.3390/fractalfract9070434.

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This study introduces a novel analytical technique known as the double local fractional Yang–Laplace transform method (LFLζ2) and rigorously investigates its foundational properties, including linearity, differentiation, and convolution. The proposed method is formulated via double local fractional integrals, enabling a robust mechanism for addressing local fractional partial differential equations defined on fractal domains, particularly Cantor sets. Through a series of illustrative examples, we demonstrate the applicability and efficacy of the LFLζ2 transform in solving complex local fractio

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Eltayeb, Hassan. "Analytic Solution of the Time-Fractional Partial Differential Equation Using a Multi-G-Laplace Transform Method." Fractal and Fractional 8, no. 8 (2024): 435. http://dx.doi.org/10.3390/fractalfract8080435.

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In several recent studies, many researchers have shown the advantage of fractional calculus in the production of particular solutions of a huge number of linear and nonlinear partial differential equations. In this research work, different theorems related to the G-double Laplace transform (DGLT) are proved. The solution of the system of time-fractional partial differential equations is addressed using a new analytical method. This technique is a combination of the multi-G-Laplace transform and decomposition methods (MGLTDM). Moreover, we discuss the convergence of this method. Two examples ar

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