Abstract
This work explores the new exact solutions of nonlinear fractional partial differential equations (FPDEs). The solutions are obtained by adopting an effective technique, the first integral method (FIM). The Riemann–Liouville (R–L) derivative and conformable derivative definitions are used to deal with fractional terms in FPDEs. The proposed method is applied to get exact solutions for space-time fractional Cahn–Allen equation and coupled space-time fractional (Drinfeld’s Sokolov–Wilson system) DSW system. The suggested technique is easily applicable and effectual, which can be implemented successfully to obtain the solutions for different types of nonlinear FPDEs.
Highlights
Fractional Calculus (FC) is an imperative field of science which deals with real number powers of the differential equations
The basic definitions, properties, and theorems of R–L and a new conformable derivative are provided in Sect
According to the definition in Eq (3), Khalil et al presented the following theorem [25], which provides some useful properties satisfied by the conformable derivative
Summary
Fractional Calculus (FC) is an imperative field of science which deals with real number powers of the differential equations. Guner et al applied the FIM to a fractional Cahn–Allen equation using Jumarie’s definition [24]. In this work, the FIM is adopted to obtain exact solutions of the nonlinear space-time fractional Cahn–Allen equation and a coupled space-time fractional DSW system.
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