On the Existence and Uniqueness of Solution of Non-linear Fractional Differential Equations with Integral Boundary Condition

In this paper, we investigate the Existence and Uniqueness of solutions of non-linear fractional boundary value differential equations with integral boundary condition using the method of Upper and Lower solutions. We employed the contraction mapping principle and Schauder fixed point theorems. We find out from the analysis that the solution of the boundary value fractional differential equation exists and is unique. An Adomian decomposition method is also used to construct the algorithm for the numerical solution of the nonlinear fractional differential equation. Further, for the implementation of the Adomian decomposition method, several numerical examples are constructed to demonstrate the applicability, accuracy, efficiency, and effectiveness of the method. The results show that the method is accurate and efficient in approximating the exact solution.