International Journal of Pure & Applied Mathematical Research

International Journal of Pure & Applied Mathematical Research

Online ISSN : 2456-7493

Frequency : Half Yearly

Current Issue : Volume 10 , Issue 1
2026

A COMPUTATIONAL–ANALYTICAL FRAMEWORK FOR SOLVING NONLINEAR FRACTIONAL MODELS IN CONTROL AND MECHANICAL SYSTEMS

Chandrashekara A C

Chandrashekara A C, Associate Professor, Department Of Mathematics, Government First Grade College

Chamarajanagara, Karnataka, India

DOI : https://doi.org/10.5281/zenodo.20544422 Page No : 13-20

Published Online : 2026-06-04

Download Full Article : PDF Check for Updates


ABSTRACT

Nonlinear fractional models have been given a lot of attention in engineering and applied sciences due to their effectiveness in describing systems with memory, hereditary behaviour and nonlocal behaviour. Fractional-order techniques contrast with classical integer-order techniques in giving a more realistic representation of complex behaviours in control and mechanical systems. Nonlinear fractional differential equations, however, are also a significant problem to solve since they are mathematically complicated, nonlinear and computationally intense. Thus, this research will create and test a computational-analytical model in the context of nonlinear fractional equations in a control and mechanical engineering application. They include exploring mathematical concepts of fractional systems, developing a combined computational-analytical solution platform and evaluating its applicability by implementing it in engineering.

The proposed framework is a combination of analytical techniques and methods like decomposition, homotopy-based methods, and numerical methods to increase the quality of the solutions and the speed of calculations. The findings indicate that the framework provides credible approximations, improved convergence qualities, as well as improved modelling qualities in comparison to the conventional methods. The work has contributed to the evolution of the fractional-order modelling since it offers a feasible method of studying nonlinear systems. It has great applications in control engineering, vibration analysis, damping systems and industrial process optimisation where accurate modelling is required, and the system must work.

Keywords: Fractional calculus, nonlinear systems, computational methods, analytical techniques, control systems, mechanical engineering.

Int. J.of Pure & App Math. Res.