Existence and uniqueness of solution for fractional differential equations with integral boundary conditions and the Adomian decomposition method

Abstract

We propose an Adomian decomposition method to solve a class of nonlinear differential equations of fractional-order with modified Caputo derivatives and integral boundary conditions. Our approach uses the integral boundary conditions to derive an equivalent nonlinear Volterra integral equation before establishing existence and uniqueness of solution and a recursion scheme for the solution. The convergence of the method is proved and an error analysis given. Two numerical examples are solved by obtaining a rapidly converging sequence of analytical functions to the solution.