Fractional Dynamic Calculus and Fractional Dynamic Equations on Time Scales

• Main Author: Georgiev, Svetlin G. (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Edition: 1st ed. 2018.
• Subjects: Calculus.; Mathematical physics.; Integral transforms.; Operational calculus.; Measure theory.; Mathematical Physics.; Integral Transforms, Operational Calculus.; Measure and Integration.

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...

Table of Contents:

• 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.