Fractional Dynamic Calculus and Fractional Dynamic Equations on Time Scales

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

1. Elements of the Time Scale Calculus.- 2. The Laplace Transform on Time Scales.- 3. The Convolution on Time Scales.- 4. The Riemann-Liouville Fractional D-Integral and the Riemann-Liouville Fractional D-Derivative on Time Scales.- 5. Cauchy Type Problem with the Riemann-Liouville Fractional D-Derivative.- 6. Riemann-Liouville Fractional Dynamic Equations with Constant Coefficients.- 7. The Caputo Fractional D-Derivative on Time Scales.- 8. Cauchy Type Problem with the Caputo Fractional D-Derivative.- 9. Caputo Fractional Dynamic Equations with Constant Coefficients.- Appendix: The Gamma Function.- Appendix: The Gamma Function.- Index.

"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 Cermák, zbMath 1410.34001, 2019)

“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)