Frontiers In Time Scales And Inequalities

This monograph contains the author's work of the last four years in discrete and fractional analysis. It introduces the right delta and right nabla fractional calculus on time scales and continues with the right delta and right nabla discrete fractional calculus in the Caputo sense. Then, it shows representation formulae of functions on time scales and presents Ostrowski type inequalities, Landau type inequalities, Grüss type and comparison of means inequalities, all these over time scales. The volume continues with integral operator inequalities and their multivariate vectorial versions using convexity of functions, again all these over time scales. It follows the Grüss and Ostrowski type inequalities involving s-convexity of functions; and also examines the general case when several functions are involved. Then, it presents the general fractional Hermite–Hadamard type inequalities using m-convexity and (s, m)-convexity. Finally, it introduces the reduction method in fractional calculus and its connection to fractional Ostrowski type inequalities is studied.

This book's results are expected to find applications in many areas of pure and applied mathematics, especially in difference equations and fractional differential equations. The chapters are self-contained and can be read independently, and advanced courses can be taught out of it. It is suitable for researchers, graduate students, seminars of the above subjects, and serves well as an invaluable resource for all science libraries.

Contents:

• Foundations of Right Delta Fractional Calculus on Time Scales
• Principles of Right Nabla Fractional Calculus on Time Scales
• About Right Delta Discrete Fractionality
• About Right Nabla Discrete Fractional Calculus
• Representations and Ostrowski Inequalities over Time Scales
• Landau Inequalities on Time Scales
• Grüss and Comparison of Means Inequalities over Time Scales
• About Integral Operator Inequalities over Time Scales
• About Vectorial Integral Operator Inequalities Using Convexity over Time Scales
• General Grüss and Ostrowski Inequalities Using s-Convexity
• Essential and s-Convexity Ostrowski and Grüss Inequalities Using Several Functions
• General Fractional Hermite–Hadamard Inequalities Using m-Convexity and (s, m)-Convexity
• About the Reduction Method in Fractional Calculus and Fractional Ostrowski Inequalities

Readership: Advanced graduate students and researchers interested in time scales, inequalities and difference/differential equations.
Key Features:

• Presents new research on time scales and related inequalities
• Materials are crucially related to difference/differential equations
• Self-contained chapters that can be read independently
• An extensive list of references is given in each chapter
• The topics covered are diverse