Overview

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.

Full Product Details

Author:   Edmundo Capelas de Oliveira
Publisher:   Springer Nature Switzerland AG
Imprint:   Springer Nature Switzerland AG
Edition:   1st ed. 2019
Volume:   240
Weight:   0.522kg
ISBN:  

9783030205263

ISBN 10:   3030205266
Pages:   321
Publication Date:   14 August 2020
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

Table of Contents

Preface; 1. A bit of history; 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 function. 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.   3. Mittag-Leffler functions. 3.1 The Mittag-Leffler function. 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.   4. Integral transforms. 4.1 Methodology. 4.2 Fourier transform. 4.3 Laplace transform. 4.4. Mellin transform. 4.5 Exercises. 4.5.1 Exercise list. 4.5.2 Suggestions. 4.5.3. Solutions. 4.5.4 Proposed exercises.   5. Fractional derivatives. 5.1 Grunwald-Letnikov derivative. 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.   6. Applications and add-ons. Forty discussed applications and complements.   Appendix. Mellin-Barnes integrals.   References. More than one hundred references   Remissive index. More than three hundred entries

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Author Information

Edmundo Capelas de Oliveira is a Professor and Researcher at the Department of Applied Mathematics at IMECC, Unicamp, Brazil. He has won the First Award for Undergraduate Teaching Incentive for outstanding teaching skills at undergraduate level in 2012. 

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