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

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