Analytic solutions for a modified fractional three wave interaction equations with conformable derivative by unified method

Abstract

The present work implements the unified method to a class of fractional partial differential systems corresponding to modified fractional three wave interaction equations (FTWIEs). The fractional derivative of the three waves envelopes is considered under the conformable sense. The conformable FTWIEs is derived in the (3 + 1) dimensions under the conformable time-fractional derivative of order α∈(0,1] based on a modification of the Lax-pair created by Zakharov-Manakov which includes three-dimensional velocity vector dotted with the usual del operator. Then, the unified method for creating solutions for nonlinear evolution FTWIEs is applied. Subsequently, a systematic algorithm is used to obtain an infinite set of exact rational solutions to the novel constructed system. By randomly selecting the special values for the parameters, three-dimensional graphs are also given for different patterns. The obtained solutions might play an essential role in many other nonlinear evolution equations that occur in the fields of engineering and mathematical physics.

Keywords

• Lax-pair
• Three wave interaction equations
• Conformable fractional derivative
• Rational solution
• Unified method