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Abstract
In this paper, we consider fractional reaction-diffusion e quations with linear and nonlinear fractional reaction ter ms in a semi-infinite domain. Using q-Homotopy Analysis Method, so lutions to these equations are obtained in the form of general recurrence relations. Closed form solutions in the form of the Mittag-Leffler function are perfectly obtained in the case with linea r fractional reaction term due to the ability to control the auxiliary par ameter h. Series solution is obtained for the case of nonlinear fract ional reaction term. Numerical analysis is presented for this cas e to display the fast convergent rate of the series solution o btained. q-HAM is a relatively simple and powerful method and has advantages over some other methods which we discuss and demonstrate for some initial value problems.
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