Fractional Dynamic Calculus and Fractional Dynamic Equations on Time Scales

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

    PDF

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. 

• 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

“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)

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

  Svetlin G. Georgiev

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

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