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All Journal Asian Journal of Science, Technology, Engineering, and Art Mikailalsys Journal of Mathematics and Statistics International Journal of Education, Management, and Technology African Multidisciplinary Journal of Sciences and Artificial Intelligence
Hussaini, Abubakar Assidiq
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Agriculture, Biological Sciences & Forestry Arts Biochemistry, Genetics & Molecular Biology Chemical Engineering, Chemistry & Bioengineering Computer Science & IT Education Electrical & Electronics Engineering Engineering Environmental Science Materials Science & Nanotechnology Mathematics Mechanical Engineering Social Sciences

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Integrated Mahgoub–VIM Hybrid Transform Technique for Solving Linear, Nonlinear, and Fractional Differential Equations Aliyu, Umar Mujahid; Kwami, A. M.; Bello, M. I.; Madaki, A. G.; Okai, J. O.; Hussaini, Abubakar Assidiq
Asian Journal of Science, Technology, Engineering, and Art Vol 4 No 3 (2026): Asian Journal of Science, Technology, Engineering, and Art
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/ajstea.v4i3.9234

Abstract

This study develops an integrated Mahgoub–Variational Iteration Method (VIM) hybrid transform technique for solving linear, nonlinear, and fractional-order ordinary and partial differential equations. The study addresses the limitations of classical integral transforms in handling nonlinearities, fractional derivatives, and memory-dependent effects, while ensuring physically consistent initial conditions through the Caputo fractional derivative. The proposed Mahgoub–VIM framework was applied to higher-order nonlinear ordinary differential equations, fractional ordinary differential equations, time-fractional partial differential equations, and fractional relaxation models. The results demonstrate rapid convergence, high stability, and close agreement with exact solutions. Comparative analysis further indicates that the proposed method consistently outperforms the Sumudu transform in terms of accuracy and error control, particularly for nonlinear and fractional problems. By avoiding linearization and discretization, the technique provides an efficient analytical framework for modeling realistic phenomena, including diffusion, heat transfer, viscoelasticity, and damping. The study contributes to the development of hybrid transform-based methods by offering a robust, accurate, and versatile analytical tool for solving complex differential systems.
Analysis of Steady Radiative MHD Nanofluid Flow in a Porous Medium: Effects of Magnetic Field, Prandtl Number, and Internal Heat Source/Sink Garba, Mohammed; Tahiru, Garba Adamu; Hussaini, Abubakar Assidiq
Mikailalsys Journal of Mathematics and Statistics Vol 4 No 2 (2026): Mikailalsys Journal of Mathematics and Statistics
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mjms.v4i2.9099

Abstract

This study presents a numerical investigation of steady magnetohydrodynamic (MHD) nanofluid flow under the combined effects of thermal radiation, Prandtl number, porous medium permeability, magnetic field strength, and internal heat generation or absorption. The objective is to examine how these governing parameters influence velocity profiles, temperature distributions, and surface heat transfer characteristics. The nonlinear partial differential equations describing coupled momentum and energy transport were reduced to a system of dimensionless ordinary differential equations through suitable similarity transformations and solved numerically. The results show that thermal radiation and internal heat generation substantially increase the temperature field, while momentum transport is suppressed due to intensified thermal–magnetic interactions and resistive forces. An increase in the Prandtl number reduces thermal diffusion and produces thinner thermal boundary layers. Higher porous medium permeability introduces porous resistance that decelerates the flow but enhances surface heat transfer through boundary layer thinning. The applied magnetic field also regulates both momentum and thermal transport through Lorentz forces. Mathematically, these trends are consistent with the structure of the dimensionless governing equations and boundary conditions, indicating strong nonlinear coupling among diffusion, convection, radiation, porous drag, and electromagnetic effects. The study concludes that surface heat transfer performance, represented by the Nusselt number, is primarily governed by wall temperature gradients. These findings contribute to the numerical understanding of MHD nanofluid transport in porous media and provide a useful theoretical basis for applications involving thermal regulation and heat transfer enhancement.
A Novel Computational Framework for Nonlinear Differential Equations Employing the Modified Laplace Adomian Polynomial Method Lukunti, Salisu; Aliyu, Umar Mujahid; Hussaini, Abubakar Assidiq; Ibrahim, Imafidor Hassan; Kolo, Mohammed Abubakar; Ahmad, Sulaiman; Hashim, Nura; Marafa, Mohammed Yusuf
International Journal of Education, Management, and Technology Vol 4 No 1 (2026): 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.v4i1.8717

Abstract

Nonlinear differential equations arise widely in applied mathematics, physics, and engineering, yet many conventional analytical and numerical methods remain limited in their ability to handle strong nonlinearities efficiently and accurately. This paper presents a novel computational framework based on the Modified Laplace–Adomian Polynomial Method (LAPM) for solving nonlinear differential equations. The proposed method integrates the Laplace transform with an enhanced form of the Adomian Decomposition Method, enabling complex nonlinear terms to be decomposed into rapidly convergent Adomian polynomials. This integration simplifies the solution procedure, reduces computational complexity, and preserves high accuracy. The performance of LAPM was validated using several benchmark nonlinear and linear differential equations, and the results demonstrated superior convergence speed, precision, and stability compared with traditional methods. The study concludes that the Modified Laplace–Adomian Polynomial Method is a reliable and efficient approach for solving a broad class of nonlinear differential equations. This work contributes to the advancement of computational methods by offering a robust alternative for the analysis of differential equation models encountered in mathematics, physics, and engineering.
A Novel Computational Framework for Nonlinear Differential Equations Employing the Modified Laplace Adomian Polynomial Method Lukunti, Salisu; Aliyu, Umar Mujahid; Hussaini, Abubakar Assidiq; Ibrahim, Imafidor Hassan; Kolo, Mohammed Abubakar; Ahmad, Sulaiman; Hashim, Nura; Marafa, Mohammed Yusuf; Yahaya, Isa
African Multidisciplinary Journal of Sciences and Artificial Intelligence Vol 3 No 1 (2026): African Multidisciplinary Journal of Sciences and Artificial Intelligence
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/amjsai.v3i1.9097

Abstract

Nonlinear differential equations pose significant challenges for conventional analytical and numerical techniques, particularly in efficiently handling complex nonlinear terms while maintaining solution accuracy and stability. This paper presents a novel computational framework for solving such equations using the Modified Laplace–Adomian Polynomial Method (LAPM), which integrates the Laplace transform with an enhanced form of the Adomian Decomposition Method. In the proposed approach, nonlinear terms are systematically decomposed into rapidly convergent Adomian polynomials, simplifying the solution process and reducing computational complexity without compromising precision. The performance of LAPM is evaluated using several benchmark nonlinear and linear differential equations, where it exhibits superior convergence speed, accuracy, and stability when compared with traditional methods. These results demonstrate that the Modified Laplace–Adomian Polynomial Method is a reliable and efficient tool for addressing a wide class of nonlinear differential equations in applied mathematics, physics, and engineering, and contributes to the growing repertoire of semi-analytical techniques for nonlinear problem solving.
Co-Authors Ahmad Sulaiman Aliyu, Umar Mujahid Bello, M. I. Garba, Mohammed Hashim, Nura Ibrahim, Imafidor Hassan Kolo, Mohammed Abubakar Kwami, A. M. Lukunti, Salisu Madaki, A. G. Marafa, Mohammed Yusuf Okai, J. O. Tahiru, Garba Adamu Yahaya, Isa