Fractional Dynamic Calculus and Fractional Dynamic Equations on Time Scales

  • Svetlin G. Georgiev
Book

Table of contents

  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 301-310
  6. Svetlin G. Georgiev
    Pages 337-344
  7. Svetlin G. Georgiev
    Pages 345-356
  8. Back Matter
    Pages 357-360

About this book

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

  • Svetlin G. Georgiev
    • 1
  1. 1.Faculty of Mathematics and InformaticsSofia University St Kliment OhridskiSofiaBulgaria

Bibliographic information

  • 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
  • Print ISBN 978-3-319-73953-3
  • Online ISBN 978-3-319-73954-0
  • About this book