Fractional partial differential equations and modified Riemann-Liouville derivative new methods for solution

Jumarie, Guy

doi:10.1007/bf02832299

Cited by 135 publications

(81 citation statements)

References 29 publications

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“…In this method, by using the transformation ξ = [14,15]. Section 3 presents the extended Kudryashov method procedure.…”

Section: Introductionmentioning

confidence: 99%

A new method for solving nonlinear fractional differential equations

Mısırlı¹,

Ege²

2017

ntmsci

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Abstract:In this paper, a new extended Kudryashov method for solving fractional nonlinear differential equations is proposed. The fractional derivative in this paper is considered in the sense of modified Riemann-Liouville. We also handle the time-fractional fifth−order Sawada−Kotera equation and the time-fractional generalized Hirota−Satsuma coupled KdV equation to illustrate the the simplicity and the effectiveness of this method. Solutions of these equations are obtained in analytical traveling wave solution form including hyperbolic and trigonometric functions.

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“…In this method, by using the transformation ξ = [14,15]. Section 3 presents the extended Kudryashov method procedure.…”

Section: Introductionmentioning

confidence: 99%

A new method for solving nonlinear fractional differential equations

Mısırlı¹,

Ege²

2017

ntmsci

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“…denotes the modified Riemann-Liouville derivative [8,9,10]; 0 < α ≤ 1 and 0 < β ≤ 1. Then, the following transforms are introduced:…”

Section: Introduction and Discussionmentioning

confidence: 99%

“…[8]. In our paper we use the modified Riemann-Liouville derivative which was defined by Jumarie [9,10,11]…”

Section: Preliminariesmentioning

confidence: 99%

Solitary Wave Solutions to Time-Fractional Coupled Degenerate Hamiltonian Equations

Katatbeh¹,

Abu-Irwaq²,

Alquran³

et al. 2014

Int. J. of Pure and Appl. Math.

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“…Some important properties and formulas can be deduced from the above, such as [35][36][37] , 0 , ) 1 (…”

Section: Description Of the Methodsmentioning

confidence: 99%

Traveling Wave Solutions for the Nonlinear Fractional Sharma-Tasso-Olever Equation

2017

International Journal of Mathematical Research

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Article History JEL Classification 35C07, 35N99. In this paper, the generalized exp(-Φ(ξ))-expansion method along with the Jumarie's modified Riemann-Liouville derivatives is proposed to solve the nonlinear fractional Sharma-Tasso-Olever (STO) equation. Consequently, the exact solutions are obtained in terms of the trigonometric, exponential, hyperbolic, and rational functions, which confirm the proposed technique is very effectual and easily applicable. Contribution/Originality:This study contributes in the existing literature on the use of the exp(-Φ(ξ))-expansion method. The method is applied to find the exact solutions to the fractional STO equation for the first time. Consequently, we get some new forms of exact solutions.

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Fractional partial differential equations and modified Riemann-Liouville derivative new methods for solution

Cited by 135 publications

References 29 publications

A new method for solving nonlinear fractional differential equations

A new method for solving nonlinear fractional differential equations

Solitary Wave Solutions to Time-Fractional Coupled Degenerate Hamiltonian Equations

Traveling Wave Solutions for the Nonlinear Fractional Sharma-Tasso-Olever Equation

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