Iterative Methods for Solving Seventh-Order Nonlinear Time Fractional Equations

Abstract

The present paper aims to investigate the numerical solutions of the seventh order Caputo fractional time Kaup-Kupershmidt, Sawada-Kotera and Lax�s Korteweg-de Vries equations using two reliable techniques, namely, the fractionalreduced differential transform method and q-homotopy analysis transform method. These equations are the mathematical formulationof physical phenomena that arise in chemistry, engineering and physics. For instance, in the motions of long waves in shallow waterunder gravity, nonlinear optics, quantum mechanics, plasma physics, fluid mechanics and so on. With these two methods, we constructseries solution to these problems in the recurrence relation form. We present error estimates to further investigate the accuracy andreliability of the proposed techniques. The outcome of the study reveals that the two techniques used are computationally accurate,reliable and easy to implement when solving fractional nonlinear complex phenomena that arise in physics, biology, chemistry andmathematics � 2022 NSP