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All Journal YASIN: Jurnal Pendidikan dan Sosial Budaya International Journal of Education, Management, and Technology
Adamu, M. M.
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Computer Science & IT Education Electrical & Electronics Engineering Engineering Materials Science & Nanotechnology Social Sciences Other

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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.
A Revised Kamal Integral Transformation Method for Solving First-Order Nonlinear Fractional Differential Equations Uba, Nura; Adamu, M. M.; Abdulhameed, M.; U, Hafsat Y.; O, Okai J.
YASIN Vol 5 No 3 (2025): JUNI
Publisher : Lembaga Yasin AlSys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/yasin.v5i3.5366

Abstract

This study integrates the Kamal transform method with Adomian polynomials to provide approximate analytical solutions for non-linear fractional differential equations. Since the Kamal transform alone cannot handle non-linear terms, Adomian polynomials are used to decompose these terms. The resulting solutions are compared with those from other methods applied to the same problems. The results show that the solution obtained with the Kamal transform and Adomian polynomial closely aligns with those from other methods, demonstrating the effectiveness of this combined approach. This work emphasizes the strength of the Kamal transform method and Adomian polynomials as integral transform techniques for solving non-linear equations.
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.
Co-Authors Abdulhameed, M. Cornelius, Michael D, Ibrahim M. Kwami, A. M. Mshelia, I. B. N, Nyikyaa M. Nasir, U. M. O, Okai J. U, Hafsat Y. Uba, Nura