A new formula for Adomian's polynomials and the analysis of its truncated series solution for fractional non-differentiable initial value problemss

Abstract

In this article, a new formula for Adomian's polynomials is introduced. It is applied to obtain the truncated series solutions for the fractional initial value problems with non-differentiable functions. This kind of equations contains a fractional single-term which is examined using Jumarie fractional derivatives and fractional Taylor series for non-differentiable functions. The property of non-locality of these equations is examined. The discuss of the existence and the uniqueness of the solutions for these equations is clarified. Also, the convergence and the error analysis of Adomian series solution of the presented formula are studied. Numerical examples are proposed to show the accuracy and the eciency of this formula for solving high-order fractional differential equations with initial values. doi:10.1017/S1446181113000321