Solving linear and non‐linear space–time fractional reaction–diffusion equations by the Adomian decomposition method

In this paper, we consider linear and non-linear space-time fractional reaction-diffusion equations (STFRDE) on a finite domain. The equations are obtained from standard reaction-diffusion equations by replacing a second-order space derivative by a fractional derivative of order β ∈ (1, 2], and a first-order time derivative by a fractional derivative of order α ∈ (0, 1]. We use the Adomian decomposition method to construct explicit solutions of the linear and non-linear STFRDE. Finally, some examples are given.

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