Volume 18, No. 6, 2021

Comparative Analy Sis Of Ordinary And Fractional Differential Equations In Modeling Physical Phenomena


Parul Boora

Abstract

This study provides a thorough comparison between fractional differential equations (FDEs) and ordinary differential equations (ODEs). In classical physics, ordinary differential equations which contain derivatives of integer order have been extensively employed to explain a variety of dynamic systems, including motion, heat conduction, and wave propagation. Nevertheless, these models frequently take local interactions and homogeneity for granted, possibly ignoring intricate memory effects and spatial interactions that are present in a lot of real-world systems. Fractional differential equations are particularly useful in capturing anomalous diffusion, viscoelastic behavior, and other non-local dynamics because they provide a more generalized framework that takes these complexities into account. Fractional differential equations incorporate derivatives of non-integer order. Through an analysis of the precision, computational effectiveness, and practicality of ODEs and FDEs in various scenarios, this research identifies the key use cases for fractional models, particularly in long-term memory or geographically diverse systems. The analysis highlights the significance of selecting the right mathematical model based on the particulars of the physical event under study, pointing out that although FDEs provide a fuller, more nuanced representation of complex systems, ODEs are more straightforward and well-established.


Pages: 9961-9969

Keywords: Ordinary Differential Equations, Fractional Differential Equations, Modelling, Physical Phenomena.

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