Modification of Picard's Iterative Method for the Solution of Fractional Differential Equations

B, Bivan J.
Aminu, Barde
O, Okai J.
G, Madaki A.
Cornelius, Michael
G, Thomas J.
N, Yohanna

Journal of Multidisciplinary Science: MIKAILALSYS
Vol 3 No 2 (2025): Journal of Multidisciplinary Science: MIKAILALSYS

A robust algorithm is introduced in the development of the Modified Picard’s Iterative Method (MPIM) to effectively address both linear and nonlinear Fractional Differential Equation (FDE) and other types of fractional order differential equations. The method's efficacy is demonstrated through numerical examples, showcasing its ability to solve these equations without resorting to linearization or small perturbations. The results affirm the method's strength, accuracy, and simplicity in comparison to alternative approaches.