Fractional reduced differential transform method based solutions of time-fractional seventh-order Sawada–Kotera–Ito equation

Abstract

Nonlinear fractional differential equations (NLFDEs) are widely used to describe various phenomena in different fields of science and engineering such as physics, chemistry, acoustics, control theory, finance, economics, mechanical, civil, electrical engineering and also in social sciences. Applications of NLFDEs can also be found in turbulence, fluid dynamics, and nonlinear biological systems. NLFDEs are believed to be potent tools to define real-world problems more accurately than the integer-order differential equations. In this investigation, we have applied fractional reduced differential transform method (FRDTM) to obtain the solution of time-fractional seventh-order Sawada–Kotera–Ito (SK-Ito) equation. The novelty of the FRDTM is that it does not require any discretization, transformation, perturbation, or any restrictive conditions. Moreover, this method requires less computation compared to other methods. Computed results are compared with the existing results for the special cases of integer as well as non-integer orders. The present results are in good agreement with the existing solutions. Here, the fractional derivatives are considered in the Caputo sense. Further, convergence analysis of the results with an increasing number of terms of the solution has also been studied.