Similarity Solution for a System of Fractional-Order Coupled Nonlinear Hirota Equations with Conservation Laws

Abstract

The analysis of differential equations using Lie symmetry has been proved a very robust tool. It is also a powerful technique for reducing the order and nonlinearity of differential equations. Lie symmetry of a differential equation allows a dynamic framework for the establishment of invariant solutions of initial value and boundary value problems, and for the deduction of laws of conservations. This article is aimed at applying Lie symmetry to the fractional-order coupled nonlinear complex Hirota system of partial differential equations. This system is reduced to nonlinear fractional ordinary differential equations (FODEs) by using symmetries and explicit solutions. The reduced equations are exhibited in the form of an Erdelyi–Kober fractional (E-K) operator. The series solution of the fractional-order system and its convergence is investigated. Noether’s theorem is used to devise conservation laws.