# Fractional Dynamic Calculus and Fractional Dynamic Equations on Time Scales

## Benefits

• Enriches understanding of fractional calculus and fractional dynamic equations

• Provides useful tools for mathematical physics applications and problems

• Suitable for graduate courses and for students new to the theory of fractional calculus

Book

1. Front Matter
Pages i-viii
2. Svetlin G. Georgiev
Pages 1-98
3. Svetlin G. Georgiev
Pages 99-156
4. Svetlin G. Georgiev
Pages 157-215
5. Svetlin G. Georgiev
Pages 217-254
6. Svetlin G. Georgiev
Pages 255-262
7. Svetlin G. Georgiev
Pages 263-299
8. Svetlin G. Georgiev
Pages 301-310
9. Svetlin G. Georgiev
Pages 311-319
10. Svetlin G. Georgiev
Pages 321-336
11. Svetlin G. Georgiev
Pages 337-344
12. Svetlin G. Georgiev
Pages 345-356
13. Back Matter
Pages 357-360

### Introduction

Pedagogically organized, this monograph introduces fractional calculus and fractional dynamic equations on time scales in relation to mathematical physics applications and problems. Beginning with the definitions of forward and backward jump operators, the book builds from Stefan Hilger’s basic theories on time scales and examines recent developments within the field of fractional calculus and fractional equations. Useful tools are provided for solving differential and integral equations as well as various problems involving special functions of mathematical physics and their extensions and generalizations in one and more variables. Much discussion is devoted to Riemann-Liouville fractional dynamic equations and Caputo fractional dynamic equations.
Intended for use in the field and designed for students without an extensive mathematical background, this book is suitable for graduate courses and researchers looking for an introduction to fractional dynamic calculus and equations on time scales.

### Keywords

fractional calculus Fractional differential equations Time-Scale Calculus Riemann-Liouville Fractional Dynamic Equations Caputo Fractional Dynamic Equations Cauchy Type Problem The Laplace Transform Convolution on Time Scales Svetlin Georgiev

#### Authors and affiliations

1. 1.Faculty of Mathematics and InformaticsSofia University St Kliment OhridskiSofiaBulgaria

Svetlin Georgiev is in the Department of Differential Equations of the Faculty of Mathematics and Informatics at Sofia University, Bulgaria.

### Bibliographic information

• Book Title Fractional Dynamic Calculus and Fractional Dynamic Equations on Time Scales
• Authors Svetlin G. Georgiev
• DOI https://doi.org/10.1007/978-3-319-73954-0
• Copyright Information Springer International Publishing AG, part of Springer Nature 2018
• Publisher Name Springer, Cham
• eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
• Hardcover ISBN 978-3-319-73953-3
• Softcover ISBN 978-3-030-08892-7
• eBook ISBN 978-3-319-73954-0
• Edition Number 1
• Number of Pages VIII, 360
• Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
• Topics
• Buy this book on publisher's site

## Reviews

“The book is self-contained and understandable to readers with a standard knowledge of basic courses in calculus and linear algebra. Also, many supporting exercises illustrate the discussed theory. On this account, this book provides a good study text in a topics course on fractional dynamic equations on time scales at the advanced undergraduate level and beginning graduate level.” (Jan Čermák, zbMath 1410.34001, 2019)