Analytical Solution of Linear Fractional Partial Differential Equation of Order 0< α ≤1 by Improved Adomian Decomposition Method

The paper aims to obtain exact analytical solution of linear nonhomogeneous space-time fractional order partial differential equation by improved Adomian decomposition method coupled with fractional Taylor expansion series. The solution of these equations are in series form may have rapid convergence to a closed-form solution. The effectiveness and sharpness of this method is shown by obtaining the exact solution of these equations with suitable initial conditions (ICs). With the help of this method, it is possible to investigate nature of solutions when we vary order of the fractional derivative. Behaviour of the solution of these equations are represented by graphs using Matlab software.