Abstract
In this paper, a new iterative method (NIM) is used to obtain the exact solutions of some nonlinear time-fractional partial differential equations. The fractional derivatives are described in the Caputo sense. The method provides a convergent series with easily computable components in comparison with other existing methods.
Highlights
In recent years, notable contributions have been made to both the theory and applications of the fractional differential equations
It is well known that the integer order differential operator is a local operator but the fractional order differential operator is non-local
We present three examples to show the efficiency and simplicity of the new iterative method
Summary
Notable contributions have been made to both the theory and applications of the fractional differential equations. There exists no method that yields an exact solution for a fractional differential equation. We use new iterative method to obtain an exact solution of following system of three nonlinear time-fractional partial differential equations [18, 19]: Dtαu = −vxwy + vywx − u, Dtαv = −wxuy − wyux + v, t > 0, 0 < α ≤ 1,.
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