ADVANCES ON FRACTIONAL DYNAMIC INEQUALITIES ON TIME SCALES

This book is devoted on recent developments of linear and nonlinear fractional Riemann-Liouville and Caputo integral inequalities on time scales. The book is intended for the use in the field of fractional dynamic calculus on time scales and fractional dynamic equations on time scales. It is also suitable for graduate courses in the above fields, and contains ten chapters. The aim of this book is to present a clear and well-organized treatment of the concept behind the development of mathematics as well as solution techniques. The text material of this book is presented in a readable and mathematically solid format.

Contents:

• Elements of Time Scale Calculus
• Elements of Fractional Dynamic Calculus on Time Scales
• Linear Inequalities for Riemann–Liouville Fractional Delta Integral Operator
• Fractional Young and Hölder Inequalities
• Fractional Inequalities for Convex Functions
• Opial-Type Inequalities
• Chebyshev-Type Inequalities
• Hardy-Type Fractional Inequalities
• Reverse Hardy-Type Fractional Inequalities
• Inequalities for Generalized Riemann-Liouville Fractional Integrals
• Appendix A: Young and Hölder Inequalities
• Appendix B: Jensen Inequalities

Readership: Undergraduate students and Graduate students in Engineering, Physics, and Biology. Researchers in ordinary differential equations.

Key Features:

• First book on fractional dynamic inequalities on time scales
• Explains the basic ideas of the theory of fractional dynamic inequalities on time scales
• Contains many examples