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All Journal YASIN: Jurnal Pendidikan dan Sosial Budaya Journal of Multidisciplinary Science: MIKAILALSYS
Cornelius, Michael
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Agriculture, Biological Sciences & Forestry Chemical Engineering, Chemistry & Bioengineering Environmental Science Physics Social Sciences Other

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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 Iterative Approach for Solving Linear Fractional-Order Delay Differential Equations D, Ibrahim M.; Adamu, M. M.; Mshelia, I. B.; Cornelius, Michael; Nasir, U. M.; O, Okai J.
YASIN Vol 5 No 2 (2025): APRIL
Publisher : Lembaga Yasin AlSys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/yasin.v5i2.5363

Abstract

This paper explores the application of the Modified New Iterative Method (MNIM) for solving linear fractional-order delay differential equations (FDDEs). The method is assessed through illustrative example, showcasing its effectiveness in producing accurate approximations for linear case, particularly when the fractional order approaches an integer. MNIM demonstrates strong performance in solving equations of integer and near-integer fractional order. However, the accuracy declines as the fractional order moves further from an integer, especially over larger intervals. MNIM remains a powerful and adaptable method for handling a broad spectrum of fractional differential equations involving delays.
Co-Authors Adamu, M. M. Aminu, Barde B, Bivan J. D, Ibrahim M. G, Madaki A. G, Thomas J. Mshelia, I. B. N, Yohanna Nasir, U. M. O, Okai J.