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Fractional Dynamic Calculus and Fractional Dynamic Equations on Time Scales

  • Book
  • © 2018

Overview

Authors:
  1. Svetlin G. Georgiev

    1. Faculty of Mathematics and Informatics, Sofia University St Kliment Ohridski, Sofia, Bulgaria

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  • 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

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-viii
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  2. Elements of Time Scale Calculus

    • Svetlin G. Georgiev
    Pages 1-98

  3. The Laplace Transform on Time Scales

    • Svetlin G. Georgiev
    Pages 99-156

  4. Convolution on Time Scales

    • Svetlin G. Georgiev
    Pages 157-215

  5. The Riemann–Liouville Fractional Δ-Integral and the Riemann–Liouville Fractional Δ-Derivative on Time Scales

    • Svetlin G. Georgiev
    Pages 217-254

  6. Cauchy-Type Problems with the Riemann–Liouville Fractional Δ-Derivative

    • Svetlin G. Georgiev
    Pages 255-262

  7. Riemann–Liouville Fractional Dynamic Equations with Constant Coefficients

    • Svetlin G. Georgiev
    Pages 263-299

  8. The Caputo Fractional Δ-Derivative on Time Scales

    • Svetlin G. Georgiev
    Pages 301-310

  9. Cauchy-Type Problems with the Caputo Fractional Δ-Derivative

    • Svetlin G. Georgiev
    Pages 311-319

  10. Caputo Fractional Dynamic Equations with Constant Coefficients

    • Svetlin G. Georgiev
    Pages 321-336

  11. Appendix: The Gamma Function

    • Svetlin G. Georgiev
    Pages 337-344

  12. Appendix: The Beta Function

    • Svetlin G. Georgiev
    Pages 345-356

  13. Back Matter

    Pages 357-360
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Keywords

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 calculusand equations on time scales. 

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)

Authors and Affiliations

  • Faculty of Mathematics and Informatics, Sofia University St Kliment Ohridski, Sofia, Bulgaria

    Svetlin G. Georgiev

About the author

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





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