Abstract
New definitions for traveling wave transformation and using of new conformable fractional derivative for converting fractional nonlinear evolution equations into the ordinary differential equations are presented in this study. For this aim we consider the time and space fractional derivatives cubic nonlinear Schrodinger equation. Then by using of the efficient and powerful method the exact traveling wave solutions of this equation are obtained. The new definition introduces a promising tool for solving many space-time fractional partial differential equations.
Highlights
The conformable fractional derivative of order α defined by the following expression and theorems
It is interesting to observe that the α -fractional derivative and the α−fractional integral are inverse of each other as given in [14,15]
The graphs of the solutions related to u1 and u2 show that with changing β the graphs of the solutions of fractional cubic nonlinear Schrodinger equation is near to graph of solution of cubic nonlinear Schrodinger equation in general form and for β = 1 it coincide with the graph of the general form of cubic nonlinear Schrodinger equation
Summary
The conformable fractional derivative of order α defined by the following expression and theorems. If f is α-differentiable in some(0, a), a > 0, and lim f α (t)exists, by definition t→0+ Let g be a function defined in the range of f and differentiable; one has the following rule: Tα (f og) (t) = t1−αg′ (t) f ′ (g (t)) .
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