Solving Systems of Fractional Partial Differential Equations via Two Dimensional Laplace Transforms

Aghili, Arman; Masomi, M. R.

doi:10.29121/granthaalayah.v5.i12.2017.528

Cited by 2 publications

(2 citation statements)

References 8 publications

(3 reference statements)

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“…Additionally, Singh et al [25] have presented the analysis of coupled fractional Burger's equations by employing a homotopy technique. In 2017, FPDEs have been handled by using Muntz-Legendre polynomial approach [26], fractional complex differential transform scheme [27], and two-dimensional Laplace transform [28]. Recently the FPDEs with Caputo-Fabrizio fractional operator have been investigated through HPTM by Gomez-Aguilar et al [29].…”

Section: Introductionmentioning

confidence: 99%

An efficient computational scheme for nonlinear time fractional systems of partial differential equations arising in physical sciences

Dubey

Kumar²,

Kumar

et al. 2020

Adv Differ Equ

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In this paper, we broaden the utilization of a beautiful computational scheme, residual power series method (RPSM), to attain the fractional power series solutions of nonhomogeneous and homogeneous nonlinear time-fractional systems of partial differential equations. This paper considers the fractional derivatives of Caputo-type. The approximate solutions of given systems of equations are calculated through the utilization of the provided initial conditions. This iterative scheme generates the fast convergent series solutions with conveniently determinable components. The implementation of this numerical scheme clearly exhibits its effectiveness, reliability and easiness regarding the procedure of the solution, as well as its better approximation. The repercussions of the fractional order of Caputo derivatives on solutions are depicted through graphical presentations for various particular cases.

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Section: Introductionmentioning

confidence: 99%

An efficient computational scheme for nonlinear time fractional systems of partial differential equations arising in physical sciences

Dubey

Kumar²,

Kumar

et al. 2020

Adv Differ Equ

View full text Add to dashboard Cite

show abstract

“…For solving partial difference equations Ozpinar and Belgacem introduced discrete homotopy perturbation Sumudu transform method in [36]. For solving partial differential equations, double Laplace transform was applied in [37,38].…”

Section: Introductionmentioning

confidence: 99%

A Transformation Method for Delta Partial Difference Equations on Discrete Time Scale

Haider

Rehman

Abdeljawad

2020

Mathematical Problems in Engineering

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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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Solving Systems of Fractional Partial Differential Equations via Two Dimensional Laplace Transforms

Abstract: In this article, the authors used two dimensional Laplace transform to solve non - homogeneous sub - ballistic fractional PDE and homogeneous systems of time fractional heat equations. Constructive examples are also provided.

Cited by 2 publications

References 8 publications

An efficient computational scheme for nonlinear time fractional systems of partial differential equations arising in physical sciences

An efficient computational scheme for nonlinear time fractional systems of partial differential equations arising in physical sciences

A Transformation Method for Delta Partial Difference Equations on Discrete Time Scale

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