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

The paper aims to obtain exact analytical solution of nonlinear nonhomogeneous space-time fractional order partial differential equationsin Gas dynamics model, Advection model,Wave model and Klein-Gordonmodel by improved Adomian decomposition method coupled with fractionalTaylor expansion series.The solution of these equations are in seriesform may have rapid convergence to a closed-form solution. The effectivenessand sharpness of this method is shown by obtaining the exactsolution of these equations with suitable initial conditions(ICs). With thehelp of this method, it is possible to investigate nature of solutions whenwe vary order of the fractional derivative. Behaviour of the solution ofthese equations are represented by graphs using MATHEMATICA software