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All Journal Mikailalsys Journal of Advanced Engineering International Mikailalsys Journal of Mathematics and Statistics
Wallen Juliet Piapna'an
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Chemical Engineering, Chemistry & Bioengineering Computer Science & IT Electrical & Electronics Engineering Engineering Mathematics Mechanical Engineering

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Robust Integral Transform Methods for the Solution of Nonlinear Fractional Ordinary Differential Equations in Viscoelastic and Biological Systems Umar Mujahid Aliyu; David Opeoluwa Oyewola; Joel John Taura; Salisu Lukunti; Hassan Muhammad; Abubakar Yahya Adamu; Abdulhalim Isah Ibrahim; Mubarak Muhammad; Imafidor Hassan Ibrahim; Mohammed Abubakar Kolo; Isah Adamu; Wallen Juliet Piapna'an; Mustapha Mohammed Mansur; Ibrahim Abubakar Adamu; Mohammed Yusuf Marafa; Abdulwasiu Umar; Sulaiman Ahmad; Nura Hashim
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.v4i2.9237

Abstract

Nonlinear and fractional-order differential equations frequently arise in viscoelastic and biological systems; however, their solution remains challenging due to the presence of nonlocal operators, memory effects, and complex boundary conditions. Classical integral transforms, including the Laplace and Fourier transforms, often have limitations in addressing these features effectively. This study presents a robust hybrid methodology that combines the Mahgoub Transform with the Variational Iteration Method (VIM) to solve nonlinear and fractional-order ordinary differential equations (ODEs). The proposed approach was systematically applied to linear, nonlinear, and fractional-order ODEs to evaluate its convergence, accuracy, and capacity to handle memory-dependent effects. The findings demonstrate that the Mahgoub–VIM method achieves rapid convergence, high accuracy, and improved performance compared with traditional transforms such as the Sumudu Transform. These results indicate that the proposed method provides a reliable and efficient analytical framework for modeling complex viscoelastic and biological phenomena governed by nonlinear and fractional-order dynamics. This study contributes to the advancement of integral transform-based solution methods and offers practical implications for the mathematical modeling of systems characterized by memory-dependent behavior and nonlinear responses.
Hybrid Integral Transform Techniques for the Solution of Third-Order Nonlinear Ordinary Differential Equations Umar Mujahid Aliyu; David Opeoluwa Oyewola; Joel John Taura; Salisu Lukunti; Hassan Muhammad; Abubakar Yahya Adamu; Abdulhalim Isah Ibrahim; Mubarak Muhammad; Imafidor Hassan Ibrahim; Mohammed Abubakar Kolo; Isah Adamu; Wallen Juliet Piapna'an; Mustapha Mohammed Mansur; Ibrahim Abubakar Adamu; Mohammed Yusuf Marafa; Abdulwasiu Umar; Sulaiman Ahmad; Nura Hashim
Mikailalsys Journal of Advanced Engineering International Vol 3 No 2 (2026): Mikailalsys Journal of Advanced Engineering International
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mjaei.v3i2.9236

Abstract

Third-order nonlinear ordinary differential equations frequently arise in the mathematical modeling of complex engineering and physical phenomena; however, exact analytical solutions remain difficult to obtain because of strong nonlinearities and higher-order derivative effects. Classical integral transform techniques, including the Laplace and Fourier transforms, are widely used for solving differential equations but often have limitations when extended to nonlinear systems. Although modern integral transforms such as the Sumudu, Mahgoub, and Elzaki transforms offer computational advantages, their applicability is generally restricted to linear models. This study introduces a hybrid analytical approach that integrates the Mahgoub transform with the Variational Iteration Method (VIM) to solve third-order nonlinear ordinary differential equations more effectively. The proposed method converts the governing equation into the transform domain and applies an iterative correction functional to address nonlinear terms without linearization or discretization. The resulting solutions are expressed in rapidly convergent series form. Numerical validation demonstrates strong agreement with exact solutions, confirming the efficiency, accuracy, and stability of the hybrid Mahgoub–VIM approach. The study concludes that this hybrid semi-analytical method provides a reliable framework for solving higher-order nonlinear differential equations in applied mathematics and engineering analysis. These findings contribute to the development of transform-based analytical methods by extending the applicability of the Mahgoub transform to nonlinear differential equation models through variational iteration.
Co-Authors Abdulhalim Isah Ibrahim Abdulwasiu Umar Abubakar Yahya Adamu David Opeoluwa Oyewola Hassan Muhammad Ibrahim Abubakar Adamu Imafidor Hassan Ibrahim Isah Adamu Joel John Taura Mohammed Abubakar Kolo Mohammed Yusuf Marafa Mubarak Muhammad Mustapha Mohammed Mansur Nura Hashim Salisu Lukunti Sulaiman Ahmad Umar Mujahid Aliyu