A Note on Double Conformable Laplace Transform Method and Singular One Dimensional Conformable Pseudohyperbolic Equations

Eltayeb, Hassan; Mesloub, Saïd; Abdalla, Yahya T.; Kılıçman, Adem

doi:10.3390/math7100949

Cited by 7 publications

(6 citation statements)

References 15 publications

(15 reference statements)

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“…Fuzzy Laplace transform was defined by [14] and then further developed and used by several authors to solve fuzzy ordinary and fuzzy partial differential equations, see for example [15][16][17][18]. Allahviranloo [19], introduced the conformable Laplace transform, and then developed by several researchers to solve conformable differential equations [20,21].…”

Section: Introduction 1research Backgroundmentioning

confidence: 99%

On Fuzzy Conformable Double Laplace Transform with Applications to燩artial Differential Equations

Abdeljawad¹,

Younus²,

Alqudah³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

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The Laplace transformation is a very important integral transform, and it is extensively used in solving ordinary differential equations, partial differential equations, and several types of integro-differential equations. Our purpose in this study is to introduce the notion of fuzzy double Laplace transform, fuzzy conformable double Laplace transform (FCDLT). We discuss some basic properties of FCDLT. We obtain the solutions of fuzzy partial differential equations (both one-dimensional and two-dimensional cases) through the double Laplace approach. We demonstrate through numerical examples that our proposed method is very successful and convenient for resolving partial differential equations.

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Section: Introduction 1research Backgroundmentioning

confidence: 99%

On Fuzzy Conformable Double Laplace Transform with Applications to燩artial Differential Equations

Abdeljawad¹,

Younus²,

Alqudah³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

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“…Some analytical and numerical methods have attracted great interest and became an important tool for differential equations with CFDs, (see previous studies 52‐80 ). Ünal et al 52 have presented a method based on the well‐known differential transform technique; it is suitable for finding the numerical solution of conformable fractional ordinary differential equations.…”

Section: Introductionmentioning

confidence: 99%

“…The single Laplace transform method was first introduced and used in Hashemi 53 . Also in Özkan and Kurt, 54 the idea was extended to the conformable double Laplace transform, and then, the new conformable fractional double Laplace transform decomposition method recommended for developing the solutions of linear and nonlinear singular one‐dimensional conformable Pseudohyperbolic and Boussinesq equations, see other works 55,56 for more detail. Analytical solutions of the conformable nonlinear time‐fractional wave equations by the Jacobi elliptic function expansion method have been investigated in Tasbozan et al 57 Furthermore, Painlevé Burgers, Nizhnik‐Novikov‐Veselov, and Klein‐Gordon equations and fractional DSW system with the CFD have been solved by using the expansion method in other works 58‐60 .…”

Section: Introductionmentioning

confidence: 99%

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Two classes of conformable fractional Sturm‐Liouville problems: Theory and applications

Mortazaasl

Akbarfam

2020

Math Methods in App Sciences

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In this paper, we investigate in more detail some useful theorems related to conformable fractional derivative (CFD) and integral and introduce two classes of conformable fractional Sturm-Liouville problems (CFSLPs): namely, regular and singular CFSLPs. For both classes, we study some of the basic properties of the Sturm-Liouville theory. In the class of r-CFSLPs, we discuss two types of CFSLPs which include left-and right-sided CFDs, each of order ∈ (n, n + 1], and prove properties of the eigenvalues and the eigenfunctions in a certain Hilbert space. Also, we apply a fixed-point theorem for proving the existence and uniqueness of the eigenfunctions. As an operator for the class of s-CFSLPs, we first derive two fractional types of the hypergeometric differential equations of order ∈ (0, 1] and obtain their analytical eigensolutions as Gauss hypergeometric functions. Afterwards, we define the conformable fractional Legendre polynomial/functions (CFLP/Fs) as Jacobi polynomial and investigate their basic properties. Moreover, the conformable fractional integral Legendre transforms (CFILTs) based on CFLP/Fs-I and-II are introduced, and using these new transforms, an effective procedure for solving explicitly certain ordinary and partial conformable fractional differential equations (CFDEs) are given. Finally, as a theoretical application, some fractional diffusion equations are solved. KEYWORDS conformable fractional derivatives and integrals, eigenvalues and eigenfunctions, fixed-point theorem, fractional diffusion, fractional Sturm-Liouville operators, transform methods JEL CLASSIFICATION

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“…Fractional partial differential equations as generalizations of classical partial differential equations, and they have been proposed and applied to many applications in various fields of physical sciences and engineering such as electromagnetic, acoustics, visco-elasticity and electro-chemistry. Recently, the solution of fractional partial differential equations has been obtained through a double Laplace decomposition method by the authors [1][2][3]. The natural transform decomposition method has been successfully used to handle linear and nonlinear problems appearing in physical and engineering disciplines [4,5].…”

Section: Introductionmentioning

confidence: 99%

A note on time-fractional Navier–Stokes equation and multi-Laplace transform decomposition method

2020

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In this study, the double Laplace Adomian decomposition method and the triple Laplace Adomian decomposition method are employed to solve one- and two-dimensional time-fractional Navier–Stokes problems, respectively. In order to examine the applicability of these methods some examples are provided. The presented results confirm that the proposed methods are very effective in the search of exact and approximate solutions for the problems. Numerical simulation is used to sketch the exact and approximate solution.

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A Note on Double Conformable Laplace Transform Method and Singular One Dimensional Conformable Pseudohyperbolic Equations

Cited by 7 publications

References 15 publications

On Fuzzy Conformable Double Laplace Transform with Applications to燩artial Differential Equations

On Fuzzy Conformable Double Laplace Transform with Applications to燩artial Differential Equations

Two classes of conformable fractional Sturm‐Liouville problems: Theory and applications

A note on time-fractional Navier–Stokes equation and multi-Laplace transform decomposition method

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