A new approach for the application of Adomian decomposition method for the solution of fractional space diffusion equation with insulated ends

This paper presents the new approach for the solution of the space fractional diffusion equation defined in finite domain by Adomian decomposition method (ADM). A typical example of special interest with fractional space derivative of order α, 1 < α ⩽ 2 is considered in the present analysis and solved by ADM after expressing the initial condition as Fourier series. The explicit solution of the space fractional diffusion equation has been presented in the closed form and then the numerical solution has been represented graphically. The behaviour of Adomian solutions and the effects of different values of α are shown graphically.