Exact solutions of space-time local fractal nonlinear evolution equations: A generalized conformable derivative approach

Hyder, Abd‐Allah; Soliman, Ahmed H.

doi:10.1016/j.rinp.2020.103135

Cited by 24 publications

(14 citation statements)

References 24 publications

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“…Equation (1) has been presented in recent paper [1] as an equation whose solution can be obtained using the method of transformation for dependent and independent variables. Equation ( 1) is the generalization of some equations describing propagation pulses in the nonlinear optics (see, for example, [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]). The purpose of this paper is to present the method for finding solutions of Equation (1) and to obtain the implicit solitary wave solutions of Equation (1) using the transformations of variables.…”

Section: Introductionmentioning

confidence: 99%

Implicit Solitary Waves for One of the Generalized Nonlinear Schrödinger Equations

Kudryashov

2021

Mathematics

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Application of transformations for dependent and independent variables is used for finding solitary wave solutions of the generalized Schrödinger equations. This new form of equation can be considered as the model for the description of propagation pulse in a nonlinear optics. The method for finding solutions of equation is given in the general case. Solitary waves of equation are obtained as implicit function taking into account the transformation of variables.

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Section: Introductionmentioning

confidence: 99%

Implicit Solitary Waves for One of the Generalized Nonlinear Schrödinger Equations

Kudryashov

2021

Mathematics

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“…To see more about the validity and applications of conformable operators, we refer to the literature. [28][29][30][31][32][33]…”

Section: Introductionmentioning

confidence: 99%

Analytical manner for abundant stochastic wave solutions of extended KdV equation with conformable differential operators

Hyder

Soliman

2021

Math Methods in App Sciences

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This work investigates the Wick‐type stochastic and extended Korteweg‐de Vries (EKdV) equation under conformable differential operators. Novel wave solutions with soliton and periodic types are produced to the deterministic EKdV under conformable differential operators. Abundant stochastic wave solutions are explored for the Wick‐type stochastic EKdV equation by using conformable differential operators and the inverse Hermite transform. The stochastic soliton and periodic solutions are denoted as functional solutions with Brownian motion environment. For the acquired solutions, comparisons and graphical representations with three‐dimensional graphs are shown for peculiar values of the existing parameters. According to the existing literature, utilization of the conformable differential operators is a novel contribution for solving the stochastic EKDV and other stochastic nonlinear problems.

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“…More precisely, the extended Zakharov-Kuzetsov equation with conformable derivative using the generalized exponential rational function method was solved in [59]. In [60], a generalized type of conformable local fractal derivative (GCFD) was employed to investigate some nonlinear evolution equations. They also set up a general technique to find exact solutions for their under studied PDEs.…”

Section: Introductionmentioning

confidence: 99%

Analytical solitons for the space-time conformable differential equations using two efficient techniques

Neirameh

Parvaneh

2021

Adv Differ Equ

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Exact solutions to nonlinear differential equations play an undeniable role in various branches of science. These solutions are often used as reliable tools in describing the various quantitative and qualitative features of nonlinear phenomena observed in many fields of mathematical physics and nonlinear sciences. In this paper, the generalized exponential rational function method and the extended sinh-Gordon equation expansion method are applied to obtain approximate analytical solutions to the space-time conformable coupled Cahn–Allen equation, the space-time conformable coupled Burgers equation, and the space-time conformable Fokas equation. Novel approximate exact solutions are obtained. The conformable derivative is considered to obtain the approximate analytical solutions under constraint conditions. Numerical simulations obtained by the proposed methods indicate that the approaches are very effective. Both techniques employed in this paper have the potential to be used in solving other models in mathematics and physics.

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Exact solutions of space-time local fractal nonlinear evolution equations: A generalized conformable derivative approach

Cited by 24 publications

References 24 publications

Implicit Solitary Waves for One of the Generalized Nonlinear Schrödinger Equations

Implicit Solitary Waves for One of the Generalized Nonlinear Schrödinger Equations

Analytical manner for abundant stochastic wave solutions of extended KdV equation with conformable differential operators

Analytical solitons for the space-time conformable differential equations using two efficient techniques

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