A Decomposition Method via a Fractional Inverse Operator for Fractional Boundary Value Problems

The current paper numerically tackles the class of fractional ordinary boundary value problems using the modification method of the classical Adomian decomposition method and through a fractional inverse operator. Among the advantages of the adopted fractional inverse operator is that the operator directly incorporates all boundary conditions without introducing unknown constants, thereby making the approximate solution valid and preferred, with the satisfaction of the involved boundary conditions. Moreover, the results of the study show that the proposed method provides exact solutions for problems that have available exact solutions, and on the other hand, gives highly accurate approximate solutions in comparison with other computational techniques, confirming its efficiency and reliability. Indeed, several comparison tables and figures are provided, assessing the effectiveness of the proposed method over existing approaches in the literature.