Integral Transform Approach for Non-Integer Order Mathematical Models

Vinod Ankushrao Yadav

Department of Mathematics, R. B. Attal College, Georai, Dist. Beed

Abstract :

Non-integer order mathematical models have gained considerable importance in representing complex dynamical processes exhibiting memory and hereditary characteristics. Classical mathematical formulations often fail to capture such nonlocal behaviors efficiently. The present work develops a transform-based analytical framework for handling generalized non-integer order systems using integral transform techniques. Fundamental concepts of non-integer operators together with commonly used derivative definitions are briefly reviewed. The study demonstrates how integral transforms convert complex operator equations into algebraic representations, enabling systematic analytical solutions. Illustrative model problems are solved to highlight the effectiveness and computational simplicity of the proposed framework. The results indicate that transform methods provide an efficient analytical tool for modeling advanced dynamic systems and offer a structured pathway for further mathematical and engineering applications.

Keywords: Integral transforms, Non-integer order systems, Mathematical modeling, Analytical methods, Dynamic systems.