Exact Solution of Space-Time Fractional Partial Differential Equations by Adomian Decomposition Method
Vidya N. Bhadgaonkar *
Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Dist. Aurangabad{431 001, India.
Bhausaheb R. Sontakke
Department of Mathematics, Pratishthan Mahavidyalaya, Paithan, Dist. Aurangabad {431 001, India.
*Author to whom correspondence should be addressed.
Abstract
The intention behind this paper is to achieve exact solution of one dimensional nonlinear fractional partial differential equation(NFPDE) by using Adomian decomposition method(ADM) with suitable initial value. These equations arise in gas dynamic model and heat conduction model. The results show that ADM is powerful, straightforward and relevant to solve NFPDE. To represent usefulness of present technique, solutions of some differential equations in physical models and their graphical representation are done by MATLAB software.
Keywords: Biological population model, Heat conduction model, fractional calculus, Adomian decomposition method, Mittage-Leffler function