Analytical approximate solution for fractional heat-like and wave-like equations with variable coefficients using the decomposition method

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 α, 0 < α ⩽ 2. The applications of the decomposition method were 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.