NEW TECHNIQUE TO ACCELERATE THE CONVERGENCE OF THE SOLUTIONS OF FRACTIONAL ORDER BRATU-TYPE DIFFERENTIAL EQUATIONS

Abstract

There are many common combination methods for solving fractional differential equations. In this work, we propose a new technique called Adomian decomposition transform method (ADTM) in order to provide a new approximate series solution of fractional order Bratu-type differential equations. The fractional order derivative is described in the Caputo sense. The ADTM is a combination of two powerful methods, the Jafari transform method and Adomian decomposition method. For accelerating the convergence of ADTM when used for these equations, we replace the nonlinear terms by their Taylor expansion. To demonstrate the efficiency and validity of the proposed method, four numerical examples are presented and we compare our obtained results with the analytical results. Finally, the numerical results obtained are represented graphically using MATLAB software.