Solitary Wave Solutions to a Fractional Model Using the Improved Modified Extended Tanh-Function Method

Abstract

Nonlinear fractional partial differential equations (NLFPDEs) are widely used in simulating a variety of phenomena arisen in several disciplines such as applied mathematics, engineering, physics, and a wide range of other applications. Solitary wave solutions of NLFPDEs have become a significant tool in understanding the long-term dynamics of these events. This article primarily focuses on using the improved modified extended tanh-function algorithm to determine certain traveling wave solutions to the space-time fractional symmetric regularized long wave (SRLW) equation, which is used to discuss space-charge waves, shallow water waves, etc. The Jumarie’s modified Riemann-Liouville derivative is successfully used to deal with the fractional derivatives, which appear in the SRLW problem. We find many traveling wave solutions on the form of trigonometric, hyperbolic, complex, and rational functions. Furthermore, the performance of the employed technique is investigated in comparison to other techniques such as the Oncoming exp(−Θ(q))-expansion method and the extended Jacobi elliptic function expansion strategy. Some obtained results are graphically displayed to show their physical features. The findings of this article demonstrate that the used approach enables us to handle more NLFPDEs that emerge in mathematical physics.