Applications and significant results of fractional calculus in the field of fluid mechanics
Qasim Khan and Anthony Suen

Department of Mathematics and Information Technology, the Education University of Hong Kong, 10 Lo Ping Road, Tai Po, N.T, Hong Kong

Abstract

My research area is applied mathematics and working on solving different complex dynamical systems under various fractional derivative operators. The existence theory, large-time behavior, and exact solutions to specific systems of partial differential equations are my study^s major areas of interest. Non-linearity is an important term in each mathematical model that needs to be handled using sophisticated approaches. The Adomian polynomial approach provides the basic and simple idea of expressing the non-linear terms, while other mathematicians have used their own procedures to do the task. The D-J polynomial provides the updated recursive polynomial without the derivative term as given in the Adomian polynomial. Once the non-linearity in a given problem is simplified, different numerical and analytical techniques are used to obtain the integer and fractional solutions to the suggested problems. For this purpose, various definitions of fractional derivatives have been used to show the fractional nature of the derivatives in the mathematical models. The present study is found very useful while dealing with various phenomena in physics, fluids, engineering, and other subjects of applied sciences using the concept of fractional calculus. The obtained results are compared using different methodologies. The solution comparison will be displayed via graphs and tables.

Keywords: Iterative Aboodh transform method- Navier Stokes equation- Atangana-Baleanu operator- Caputo operator- Caputo-Fabrizio operator.

Topic: Physical Education