Analytical approximate solution for fractional heat-like and wave-like equations with variable coefficients using the decomposition method. (English) Zbl 1070.65105

Summary: The time fractional heat-like and wave-like equations with variable coefficients are obtained by replacing the first order and second order time derivative by a fractional derivative of order \(\alpha\), \(0 < \alpha \leqslant 2\). The applications of the decomposition method are extended to derive analytical solutions in the form of a series with easily computed terms for these generalized fractional equation. Some examples are presented to show the efficiency and simplicity of the method.


65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35K55 Nonlinear parabolic equations
35L70 Second-order nonlinear hyperbolic equations
26A33 Fractional derivatives and integrals
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