A novel analytical method for time-fractional differential equations

Kaplan, Melike; Bekir, Ahmet

doi:10.1016/j.ijleo.2016.05.152

Cited by 80 publications

(21 citation statements)

References 18 publications

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“…Remark 2 If we compare our results with the results obtained by [60,61], we can see that our solutions of Eq. (1.2) are new and satisfy the equation.…”

Section: (3 + 1)-dimensional Kdv-zk Equation With Time-fractional Dersupporting

confidence: 53%

Solitary and periodic wave solutions of higher-dimensional conformable time-fractional differential equations using the ( G ′ G , 1 G

et al. 2018

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In this paper, the two variables ( G G , 1 G )-expansion method is applied to obtain new exact solutions with parameters of higher-dimensional nonlinear time-fractional differential equations (NTFDEs) in the sense of the conformable fractional derivative. To clarify the veracity of this method, it is implemented in nonlinear (2 + 1)-dimensional time-fractional biological population (BP) model and nonlinear (3 + 1)-dimensional KdV-Zakharov-Kuznetsov (KdV-ZK) equation with time-fractional derivative. When the parameters take some special values, the solitary and periodic solutions are obtained from the hyperbolic and trigonometric function solutions.

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“…Remark 2 If we compare our results with the results obtained by [60,61], we can see that our solutions of Eq. (1.2) are new and satisfy the equation.…”

Section: (3 + 1)-dimensional Kdv-zk Equation With Time-fractional Dersupporting

confidence: 53%

Solitary and periodic wave solutions of higher-dimensional conformable time-fractional differential equations using the ( G ′ G , 1 G

et al. 2018

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“…Previously, many authors had tackled the fractional Sharma-Tasso-Olver equation in different approaches. For example, finding exact solutions of the fractional Sharma-Tasso-Olver equation in the sense of the modified Riemann-Liouville derivative using the (G /G, 1/G)-expansion method [56], the tanh ansatz method [57], the exp(−Φ(ξ)) method [58], the sub-equation method [59], and the improved extended tanh-coth method [13]. In addition, constructing exact solutions of the nonlinear conformable time Sharma-Tasso-Olver equation via conformable derivatives was done using the simplest equation method [60] and the direct algebraic method [61].…”

Section: Discussionmentioning

confidence: 99%

New Exact Solutions of the Conformable Space-Time Sharma–Tasso–Olver Equation Using Two Reliable Methods

2020

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The major purpose of this article is to seek for exact traveling wave solutions of the nonlinear space-time Sharma–Tasso–Olver equation in the sense of conformable derivatives. The novel ( G ′ G ) -expansion method and the generalized Kudryashov method, which are analytical, powerful, and reliable methods, are used to solve the equation via a fractional complex transformation. The exact solutions of the equation, obtained using the novel ( G ′ G ) -expansion method, can be classified in terms of hyperbolic, trigonometric, and rational function solutions. Applying the generalized Kudryashov method to the equation, we obtain explicit exact solutions expressed as fractional solutions of the exponential functions. The exact solutions obtained using the two methods represent some physical behaviors such as a singularly periodic traveling wave solution and a singular multiple-soliton solution. Some selected solutions of the equation are graphically portrayed including 3-D, 2-D, and contour plots. As a result, some innovative exact solutions of the equation are produced via the methods, and they are not the same as the ones obtained using other techniques utilized previously.

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“…In order to find the exact solutions of nonlinear PDEs, many powerful methods have been developed. A few of the methods are: the sub-equation method [8][9][10], the modified simple equation method [11], the exp(−φ(ξ)) method [12,13], homotopy analysis method [14,15] , first integral method [16,17], G/G expansion method [18][19][20], the functional variable method [21,22], the improved tan φ 2 -expansion method [23,24], etc.…”

Section: Introductionmentioning

confidence: 99%

Soliton Solutions of Mathematical Physics Models Using the Exponential Function Technique

et al. 2020

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This paper is based on finding the exact solutions for Burger’s equation, Zakharov-Kuznetsov (ZK) equation and Kortewegde vries (KdV) equation by utilizing exponential function method that depends on the series of exponential functions. The exponential function method utilizes the homogeneous balancing principle to find the solutions of nonlinear equations. This method is simple, wide-reaching and helpful for finding the exact solution of nonlinear conformable PDEs.

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A novel analytical method for time-fractional differential equations

Cited by 80 publications

References 18 publications

Solitary and periodic wave solutions of higher-dimensional conformable time-fractional differential equations using the ( G ′ G , 1 G

Solitary and periodic wave solutions of higher-dimensional conformable time-fractional differential equations using the ( G ′ G , 1 G

New Exact Solutions of the Conformable Space-Time Sharma–Tasso–Olver Equation Using Two Reliable Methods

Soliton Solutions of Mathematical Physics Models Using the Exponential Function Technique

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