Progress in Fractional Differentiation & Applications

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In this paper, the conformable time-fractional derivative of order α ∈ (0,1] is considered, instead of the classical time derivative for α = 1, in view of the Lax-pair operator that leads to a fractional nonlinear evolution system of four-wave-interaction-equations (4-WIEs). The resulted system is then solved by an ansatz contains tan and secant hyperbolic functions with complex coefficients. A systematic steps are introduced to obtain a general form of exact soliton solutions for the resulted system in (1+1) one spatial and one temporal dimensions. We showed that the obtained solutions could be modified to represent solutions of a similar system but in (2+1) two spatial and one temporal dimensions too. In fact, our suggested ansatz can be used to obtain exact soliton solutions for fractional N-wave-interaction-equations (N-WIEs) in one or more spatial dimensions for N greater than or equal to four. Eventually, some numerical examples are stated with 3D graphs to give a better understanding of the behavior of the soliton waves while the interaction is turned on.

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