A Modified Optimized Decomposition Method for Solving Nonlinear Fractional Two-Point Boundary Value Problems With Dirichlet Boundary Conditions

A new modified approach for solving nonlinear fractional-order ordinary differential equations of two-point boundary value problems with Dirichlet boundary conditions is introduced in this research. This approach is mainly based on integrating the optimized decomposition method with a modified Duan-Rach recursion scheme. This technique is an extension of the modified Duan-Rach Adomian decomposition method presented in previous work because the optimized decomposition method is considered a modification of the well-known classical Adomian decomposition method. To demonstrate the computation efficiency of the proposed method, numerical examples are provided. The results of using this method on the cases that were studied demonstrate its high accuracy, simplicity, and effectiveness.