New Rational Solutions of fractional–order Sharma–Tasso–Olever equation with Atangana–Baleanu derivative arising in physical sciences

Abstract

It is renowned fact that the study of nonlinear partial differential equations (NPDEs) play a vital rule in cosmic phenomena, atomic and matter physics, that is why researchers have a keen interest to study and find their solutions. Sharma–Tasso–Olever equation is such type of an important equation. In this article, we consider the fractional-order Sharma–Tasso–Olever equation with non-singular Atangana–Baleanu derivative and utilize three remarkable analytical methods, namely, the homotopy perturbation method (HPM), the homotopy perturbation method with Laplace transform (HPLM), and the Adomian decomposition method (ADM), for obtaining the rational solutions. To get a better understanding of this new derivative operator with these methods, the achieved results are compared with the existing results in the literature of Caputo derivative. The numerical results reveal the efficiency, reliability, significant features, and simple in computation with high accuracy by using Atangana–Baleanu derivative with these three approaches. These three methods can be used to find the analytical solutions of many other fractional order problems with Atangana–Baleanu derivative in science and engineering.