Solved Exercises in Fractional Calculus (Studies in Systems, Decision and Control)

Description

This book contains a brief historical introduction and state of the art in fractional calculus. The author introduces some of the so-called special functions, in particular, those which will be directly involved in calculations. The concepts of fractional integral and fractional derivative are also presented. Each chapter, except for the first one, contains a list of exercises containing suggestions for solving them and at last the resolution itself. At the end of those chapters there is a list of complementary exercises. The last chapter presents several applications of fractional calculus. Foreword I Foreword II Foreword III Preface Contents 1 A Bit of History 1.1 Historical Survey 1.1.1 Period from 1695 to 1975 1.1.2 Period from 1976 to 1993 1.1.3 Period from 1994 to 2015 1.1.4 Period After 2015 References 2 Special Functions 2.1 Functions and Pochhammer Symbol 2.2 Hypergeometric Function and Particular Cases 2.3 Confluent Hypergeometric Function and Particular Cases 2.4 Generalized Hypergeometric Functions 2.4.1 Wright Functions 2.4.2 Meijer's G-Function 2.4.3 Fox's H-Function 2.5 Exercises 2.5.1 Exercise list 2.5.2 Suggestions 2.5.3 Solutions 2.5.4 Proposed Exercises References 3 Mittag-Leffler Functions 3.1 Mittag-Leffler Functions 3.2 Wright and Mainardi Functions 3.3 Exercises 3.3.1 Exercise List 3.3.2 Suggestions 3.3.3 Solutions 3.3.4 Proposed Exercises References 4 Integral Transforms 4.1 Methodology 4.2 Fourier Transform 4.2.1 Properties 4.3 Laplace Transform 4.3.1 Properties 4.3.2 Bromwich and Hankel Contours 4.3.3 Inverse Laplace Transform 4.3.4 Theorems of Initial Value and Final Value 4.4 Mellin Transform 4.5 Exercises 4.5.1 Exercise List 4.5.2 Sugestions 4.5.3 Solutions 4.5.4 Proposed Exercises References 5 Fractional Derivatives 5.1 Grünwald-Letnikov Formulation 5.2 Integer Order Integral 5.3 Riemann-Liouville and Hadamard Integrals 5.4 Riemann-Liouville, Caputo and Hadamard Derivatives 5.5 Exercises 5.5.1 Exercise list 5.5.2 Suggestions 5.5.3 Solutions 5.5.4 Proposed exercises References 6 Applications and Add-ons References A Mellin-Barnes Integrals References Index