A new semi-analytical method for solving a class of time fractional partial differential equations with variable coefficients

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We present a new numerical method for solving a wide class of time fractional partial differential equations with a space operator of general form. The proposed method is based on the Fourier series expansion along the spatial coordinate which transforms the original time fractional partial differential equations into a sequence of multi-term fractional ordinary differential equations. The fractional ordinary differential equations are solved by the use of an efficient numerical technique. The numerical examples confirm the high accuracy and efficiency of the proposed numerical scheme.