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Solved Exercises in Fractional Calculus Edmundo Capelas de Oliveira

Solved Exercises in Fractional Calculus By Edmundo Capelas de Oliveira

Solved Exercises in Fractional Calculus by Edmundo Capelas de Oliveira

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Summary

This book contains a brief historical introduction and state of the art in fractional calculus. 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.

Solved Exercises in Fractional Calculus Summary

Solved Exercises in Fractional Calculus by Edmundo Capelas de Oliveira

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.

About Edmundo Capelas de Oliveira

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.

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

Additional information

NLS9783030205263
9783030205263
3030205266
Solved Exercises in Fractional Calculus by Edmundo Capelas de Oliveira
Edmundo Capelas de Oliveira
Studies in Systems, Decision and Control
New
Paperback
Springer Nature Switzerland AG
2020-08-14
321
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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