Travelling Wave Solutions for Some Time-Fractional Nonlinear Differential Equations

Abstract

The study employs the potent generalized Kudryashov method to address challenges posed by fractional differential equations in mathematical physics. The primary focus is on deriving new exact solutions for three significant equations: the (3+1)-dimensional time fractional Jimbo-Miwa equation, the (3+1)-dimensional time fractional modified KdV-Zakharov-Kuznetsov equation and the (2+1)-dimensional time fractional Drinfeld-Sokolov-Satsuma-Hirota equation. The versatility and efficacy of the Kudryashov method in addressing complex nonlinear problems establish it as a pivotal component in our research. Specifically, we delineate fractional derivatives within the framework of the conformable fractional derivative, thereby laying a robust foundation for our mathematical inquiries. This paper investigates the efficacy of the generalized Kudryashov method in addressing the intricate challenges posed by fractional differential equations.