A REVIEW ON FRACTIONAL CALCULUS AND ITS APPLICATIONS IN ENGINEERING
C. I. Perera*
Institute of Technology University of Moratuwa, Sri Lanka
Session: Technical Session E
Abstract
The main purpose of this research is to explore the evolution of fractional calculus from its inception to its diverse applications in science and engineering. The concept of calculus dates back to the work of Sir Isaac Newton, an English mathematician, and Gottfried Leibniz, a French mathematician who presented similar ideas using different notations. Initially, the order of differentiation was understood as an integer. However, as time progressed, mathematicians encountered a paradox: what if the order of a derivative were not an integer but a fraction? This question marked the beginning of fractional calculus. Over the years, a lot of definitions were developed by renowned mathematicians such as Euler, Lagrange, and Laplace. In its early stages, fractional calculus was primarily theoretical with little application to practical problems. However, as the field matured, mathematicians began to apply this theory to practical situations. Today, fractional calculus has seen rapid development and application across various domains in science and engineering. Some applications are shortlisted as follows. In the field of computer and electrical engineering fractional calculus is used in noise filtering processes, particularly in echocardiographic imaging, to minimize noise interference. It also plays a crucial role in developing de-noising models in digital imaging. In mineral engineering, leaching column test is conducted by using new rate equation formed by fractional calculus. The Behaviour of Hydrological processes on Earth has been mathematically modelled using fractional calculus. In the field of quantum mechanics, the Schrödinger equation has been further improved using the fractional calculus theory in the formation of a new version of the fractional Schrödinger equation in the context of space-time.
Keywords: Fractional calculus, fractional derivative, fractional integral.
DOI: 10.64752/PXVK5878