Exact solutions for fractional DDEs via auxiliary equation method coupled with the fractional complex transform

Aslan, İsmail

doi:10.1002/mma.3946

Cited by 23 publications

(6 citation statements)

References 39 publications

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“…Some examples of approaches for obtaining approximate solutions in an analytical form to NPDEs are the Adomian decomposition method (ADM) [1,2], the variational iteration method (VIM) [3,4], the differential transform method (DTM) [5], and the homotopy perturbation method (HPM) [6,7]. Some algorithms for obtaining explicit exact solutions of NPDEs are, for instance, the ( G G )-expansion method [8,9], the ( G G , 1 G )-expansion method [10], the fractional Riccati expansion method [11,12], the improved extended tanh-coth method [13], the Kudryashov method [14,15], and the sub-equation method [16,17]. All of the above methods are based on the homogeneous balance principle.…”

Section: Introductionmentioning

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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Section: Introductionmentioning

confidence: 99%

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

2020

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“…In many research fields, more and more attention has been paid to fractional-order models [60][61][62][63][64][65][66][67][68][69][70][71][72][73][74][75][76]. Recently, Aslan [77][78][79][80] has successfully extended analytical methods-combined symbolic computation to solve fractional semidiscrete equations. How to extend the method used in this paper to such fractional semidiscrete equations is also worthy of studying.…”

Section: Introductionmentioning

confidence: 99%

Analytical Insights into a Generalized Semidiscrete System with Time-Varying Coefficients: Derivation, Exact Solutions, and Nonlinear Soliton Dynamics

Zhang

Zhao

2020

Complexity

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In this paper, a new generalized semidiscrete integrable system with time-varying coefficients is analytically studied. Firstly, the generalized semidiscrete system is derived from a semidiscrete matrix spectral problem by embedding finite time-varying coefficient functions. Secondly, exact and explicit N-soliton solutions of the semidiscrete system are obtained by using the inverse scattering analysis. Finally, three special cases when N=1,2,3 of the obtained N-soliton solutions are simulated by selecting some appropriate coefficient functions. It is shown that the time-varying coefficient functions affect the spatiotemporal structures and the propagation velocities of the obtained semidiscrete one-soliton solutions, two-soliton solutions, and three-soliton solutions.

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“…Also, these three methods are compared for Fitzhugh-Nagumo equation. 7 Besides, homotopy analysis method (HAM) 8,9 for fractional wave equations and fractional Whitham-Broer-Kaup equation, the implicit quadrature method 10 for ordinary fractional differential equations, Godunov-type methods, 11,12 reproducing kernel method (RKM) [13][14][15][16][17][18][19][20] for partial fractional differential equations, integrodifferential equations, Bagley-Torvik and Painleve equations, and Tricomi and Keldysh equations, local fractional integral iterative method 21 for fractional wave equations, and auxiliary equation method 22 for fractional differential-difference equations are suggested.…”

Section: Introductionmentioning

confidence: 99%

Comparison of two reliable methods to solve fractional Rosenau‐Hyman equation

Şenol

Taşbozan

Kurt

2019

Math Methods in App Sciences

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In this study, we examine the numerical solutions of the time-fractional Rosenau-Hyman equation, which is a KdV-like model. This model demonstrates the formation of patterns in liquid drops. For this purpose, two reliable methods, residual power series method (RPSM) and perturbation-iteration algorithm (PIA), are used to obtain approximate solutions of the model. The fractional derivative is taken in the Caputo sense. Obtained results are compared with each other and the exact solutions both numerically and graphically. The outcome shows that both methods are easy to implement, powerful, and reliable. So they are ready to implement for a variety of partial fractional differential equations.

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Exact solutions for fractional DDEs via auxiliary equation method coupled with the fractional complex transform

Cited by 23 publications

References 39 publications

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

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

Analytical Insights into a Generalized Semidiscrete System with Time-Varying Coefficients: Derivation, Exact Solutions, and Nonlinear Soliton Dynamics

Comparison of two reliable methods to solve fractional Rosenau‐Hyman equation

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