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Rational exp($−\psi(\eta)$)-expansion method; coupled Higgs equation; Maccari system; travelling wave solutions; fractional calculus; Caputo’s fractional derivative.

In this article, a variety of solitary wave solutions are found for some nonlinear equations. In mathematical physics, we studied two complex systems, the Maccari system and the coupled Higgs field equation. We construct sufficient exact solutions for nonlinear evolution equations. To study travelling wave solutions, we used a fractional complex transform to convert the particular partial differential equation of fractional order into the corresponding partial differential equation and the rational exp$(−\psi(\eta)$)-expansion method is implemented tofind exact solutions of nonlinear equation. We find hyperbolic, trigonometric, rational and exponential function solutions using the above equation. The results of various studies show that the suggested method is very effectiveand can be used as an alternative for finding exact solutions of nonlinear equations in mathematical physics. A comparative study with the other methods gives validity to the technique and shows that the method providesadditional solutions. Graphical representations along with the numerical data reinforce the efficacy of the procedure used. The specified idea is very effective, pragmatic for partial differential equations of fractional order andcould be protracted to other physical phenomena.

AYYAZ ALI¹ MUHAMMAD ASAD IQBAL² SYED TAUSEEF MOHYUD-DIN¹

1. Department of Mathematics, Faculty of Sciences, HITEC University, Taxila, Pakistan
2. Department of Mathematics, Mohi-ud-din Islamic University, Nerain Sharif, AJ&K

Published

16 November 2016

Manuscript received

27 July 2015

Manuscript revised

22 December 2015

Accepted

25 January 2016

Early published

18 October 2016