© 2018

Fractional Dynamic Calculus and Fractional Dynamic Equations on Time Scales


  • 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


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


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. 


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

About the authors

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

Bibliographic information


“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)