Analytical Solution of Nonlinear Nonhomogeneous Space and Time Fractional Physical Models by Improved Adomian Decomposition Method

Abstract

The paper aims to obtain exact analytical solution of nonlinear nonhomogeneous space-time fractional order partial differential equations in Gas dynamics model, Advection model, Wave model and Klein-Gordon model 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 MATHEMATICA software.