Computational Fractional Dynamical Systems: Fractional Differential Equations And Applications

The subject of fractional calculus has gained considerable popularity and importance during the past three decades, mainly due to its validated applications in various fields of science and engineering. It deals with differential and integral operators with non-integral powers. The fractional derivative has been used in various physical problems, such as frequency-dependent damping behavior of structures, motion of a plate in a Newtonian fluid, controller for dynamical systems, etc. Also, the mathematical models in electromagnetics, rheology, viscoelasticity, electrochemistry, control theory, Brownian motion, signal and image processing, fluid dynamics, financial mathematics, and material science are well defined by fractional-order differential equations. It is sometimes challenging to obtain the solution (both analytical and numerical) of nonlinear partial differential equations of fractional order. Therefore, for the last few decades, a great deal of attention has been directed towards the solution of these kinds of problems. Researchers are trying to develop various efficient methods to handle these problems. A few methods have been developed by other researchers to analyze the above problems, but those are sometimes problem-dependent and are not efficient. Therefore, the development of appropriate computational efficient methods and their use in solving the mentioned problems is the current challenge. While some books are dedicated to providing particular computational methods for solving these kinds of models, the content of these books are limited and do not cover all the aspect of computationally efficient methods regarding fractional-order systems. In this regard, this book is an attempt to rigorously present a variety of computationally efficient methods (around 25) in one place. Various semi-analytical and expansion methods with respect to the main title of the book are addressed to solve different types of fractional models. Here, the author's aim is to include different numerical methods with detailed steps to handle basic and advanced equations arising in science and engineering.