Some Nonlinear Fractional PDEs Involving - Derivative by Using Rational - Expansion Method

Haifa Bin Jebreen

Complexity, 2020, vol. 2020, 1-22

Abstract:

In this article, some new nonlinear fractional partial differential equations (PDEs) (the space-time fractional order Boussinesq equation; the space-time (2 + 1)-dimensional breaking soliton equations; and the space-time fractional order SRLW equation) have been considered, in which the treatment of these equations in the diverse applications are described. Also, the fractional derivatives in the sense of - derivative are defined. Some fractional PDEs will convert to consider ordinary differential equations (ODEs) with the help of transformation - derivative. These equations are analyzed utilizing an integration scheme, namely, the rational - expansion method. Different kinds of traveling wave solutions such as solitary, topological, dark soliton, periodic, kink, and rational are obtained as a by product of this scheme. Finally, the existence of the solutions for the constraint conditions is also shown. The outcome indicates that some fractional PDEs are used as a growing finding in the engineering sciences, mathematical physics, and so on.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:hin:complx:9179826

DOI: 10.1155/2020/9179826

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