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

Momani, Shaher

Appl. Math. Comput. 165, No. 2, 459-472 (2005).

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.

MSC:

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

Keywords:

wave-like equation; heat-like equation; Adomian decomposition method; fractional calculus; numerical example

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