Numerical and Analytical Method for Solution of Fractional Differential Equations

Abstract

Fractional differ-integrals plays very important role in the description of the dynamics of many complex systems. Many methods were proposed to explicit solution in the last two decades but rigorous convergence analysis is often not available. Thus a user who needs a systematic approach for a particular problem often has difficulties in finding suitable method. The development of suitable and well-founded new analytical and approximate methods to solve complicated Fractional ordinary and partial differential equations has become the major attraction amongst researchers. In the present paper the fractional reduced differential transform method (FRDTM) is implemented to solve linear and nonlinear initial and boundary value problems for time fractional differential equations. The relation of solution with time at given x=1 and the phase plot of solution behavior for different derivative orders like 0.5, 0.75 and 1 are depicted through graphs.