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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
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mikailalsys.v3i2.5314

Abstract

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.
A Modified New Iterative Method for Solving Nonlinear Fractional-Order Delay Differential Equations D, Ibrahim M.; Adamu, M. M.; Mshelia, I. B.; Kwami, A. M.; O, Okai J.; N, Nyikyaa M.
International Journal of Education, Management, and Technology Vol 3 No 2 (2025): International Journal of Education, Management, and Technology
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/ijemt.v3i2.5381

Abstract

This paper explores the application of the Modified New Iterative Method (MNIM) to solve nonlinear fractional-order delay differential equations (NFDDEs). A series of test problems are presented to evaluate the method's performance across various fractional orders. The results indicate that MNIM yields highly accurate approximations, particularly when the fractional order approaches an integer. The method is especially effective for integer-order cases and for fractional orders close to them. However, its accuracy decreases as the fractional order becomes smaller, with noticeable errors emerging over larger domains. MNIM remains a powerful and adaptable approach for solving a broad class of fractional differential equations.