Edmundo Capelas de Oliveira
Springer International Publishing
e druk, 2019
9783030205232
Solved Exercises in Fractional Calculus
Specificaties
Gebonden, blz.
|
Engels
Springer International Publishing |
e druk, 2019
ISBN13: 9783030205232
Rubricering
Onderdeel van serie
Studies in Systems, Decision and Control
Verwachte levertijd ongeveer 9 werkdagen
Samenvatting
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.
Specificaties
ISBN13:9783030205232
Taal:Engels
Bindwijze:gebonden
Uitgever:Springer International Publishing
Inhoudsopgave
<p>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.</p>
<p> </p>
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.<p></p>
<p> </p>
<p>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.</p>
<p> </p>
<p>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.</p>
<p> </p>
<p>6. Applications and add-ons. Forty discussed applications and complements.</p>
<p> </p>
<p>Appendix. Mellin-Barnes integrals.</p>
<p> </p>
<p>References. More than one hundred references</p>
<p> </p>
<p>Remissive index. More than three hundred entries</p>
<p> </p>
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.<p></p>
<p> </p>
<p>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.</p>
<p> </p>
<p>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.</p>
<p> </p>
<p>6. Applications and add-ons. Forty discussed applications and complements.</p>
<p> </p>
<p>Appendix. Mellin-Barnes integrals.</p>
<p> </p>
<p>References. More than one hundred references</p>
<p> </p>
<p>Remissive index. More than three hundred entries</p>