A novel analytical technique to obtain the solitary solutions for nonlinear evolution equation of fractional order

Abdul Ghaffar,Sarfaraz Ahmed,Dumitru Baleanu,Ayyaz Ali,Saima Akram,Kottakkaran Sooppy Nisar,Moin-Ud-Din Junjua

doi:10.1186/s13662-020-02751-5

Abstract

We investigate some solitary wave results of time fractional evolution equations. By employing the extended rational exp ( (-frac{{psi }^{prime }}{psi }) ( eta ) )-expansion method, a few different results including kink, singular-kink, multiple soliton, and periodic wave solutions are formally generated. It is worth mentioning that the solutions obtained are more general with more parameters. The exact solutions are constructed in the form of exponential, trigonometric, rational, and hyperbolic functions. With the choice of proper values of parameters, graphs to some of the obtained solutions are drawn. On comparing some special cases, our solutions are in good agreement with the results published previously and the remaining are new.

Highlights

In the exceptional development of nonlinear sciences and engineering, during the last few decades, many researchers seem to be interested in obtaining exact and numerical solutions for nonlinear partial differential (NLPD) equations
The study of exact solutions of nonlinear evolution equations plays a major role to explore the internal mechanism of nonlinear phenomena [3, 13]
Fractional calculus is a dominant tool in several nonlinear fields such as plasma physics, fluid mechanics, solid-state physics, optical fibers, quantum field theory, biophysics, chemical kinematics, electricity, chemistry, biology, geochemistry, Ghaffar et al Advances in Difference Equations

Summary

Introduction

In the exceptional development of nonlinear sciences and engineering, during the last few decades, many researchers seem to be interested in obtaining exact and numerical solutions for nonlinear partial differential (NLPD) equations. Fractional calculus is a dominant tool in several nonlinear fields such as plasma physics, fluid mechanics, solid-state physics, optical fibers, quantum field theory, biophysics, chemical kinematics, electricity, chemistry, biology, geochemistry, Ghaffar et al Advances in Difference Equations (2020) 2020:308 propagation of shallow water waves and engineering [7, 10, 16]. For this purpose many techniques were used such as the homogeneous balance method [17], the exp-function method [18], the improved extended F-expansion method [19], and the homotopy perturbation method [20].

Description of method

Analogy and analysis

Conclusions

Methods