Fractional Differential Equations Numerical Methods For Applications
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Fractional Differential Equations
This book is a landmark title in the continuous move from integer to non-integer in mathematics: from integer numbers to real numbers, from factorials to the gamma function, from integer-order models to models of an arbitrary order. For historical reasons, the word 'fractional' is used instead of the word 'arbitrary'.This book is written for readers who are new to the fields of fractional derivatives and fractional-order mathematical models, and feel that they need them for developing more adequate mathematical models.In this book, not only applied scientists, but also pure mathematicians will find fresh motivation for developing new methods and approaches in their fields of research.A reader will find in this book everything necessary for the initial study and immediate application of fractional derivatives fractional differential equations, including several necessary special functions, basic theory of fractional differentiation, uniqueness and existence theorems, analytical numerical methods of solution of fractional differential equations, and many inspiring examples of applications. - A unique survey of many applications of fractional calculus - Presents basic theory - Includes a unified presentation of selected classical results, which are important for applications - Provides many examples - Contains a separate chapter of fractional order control systems, which opens new perspectives in control theory - The first systematic consideration of Caputo's fractional derivative in comparison with other selected approaches - Includes tables of fractional derivatives, which can be used for evaluation of all considered types of fractional derivatives
Fractional Differential Equations: Numerical Methods for Applications
Fractional calculus is a branch of mathematical analysis that studies the different possibilities of defining real number powers or complex number powers of the differentiation operator and the integration operator. It also focuses on developing a calculus for such operators generalizing the classical one. Fractional differential equations are a generalization of differential equations through the application of fractional calculus. They are also referred to as extraordinary differential equations. They are widely used in various disciplines such as mathematics, physics, chemistry, biology, medicine, mechanics, control theory, signal and image processing, and environmental science. Most of the computational tools do not have in-built functions for solving fractional differential equations or differential equations having non-integer order. However, there are certain numerical methods for solving fractional-order problems such as certain MATLAB routines. This book provides a broad overview of the numerical methods used for solving fractional differential equations. It will serve as a valuable source of reference for students and mathematics researchers.
Fractional Calculus
This title will give readers the possibility of finding very important mathematical tools for working with fractional models and solving fractional differential equations, such as a generalization of Stirling numbers in the framework of fractional calculus and a set of efficient numerical methods.