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Full Description
The concept of derivatives of non-integer order, known as fractional derivatives, first appeared in the letter between L'Hopital and Leibniz in which the question of a half-order derivative was posed. Since then, many formulations of fractional derivatives have appeared. Recently, a new definition of fractional derivative, called the "fractional conformable derivative," has been introduced. This new fractional derivative is compatible with the classical derivative and it has attracted attention in areas as diverse as mechanics, electronics, and anomalous diffusion.
Conformable Dynamic Equations on Time Scales is devoted to the qualitative theory of conformable dynamic equations on time scales. This book summarizes the most recent contributions in this area, and vastly expands on them to conceive of a comprehensive theory developed exclusively for this book. Except for a few sections in Chapter 1, the results here are presented for the first time. As a result, the book is intended for researchers who work on dynamic calculus on time scales and its applications.
Features
Can be used as a textbook at the graduate level as well as a reference book for several disciplines
Suitable for an audience of specialists such as mathematicians, physicists, engineers, and biologists
Contains a new definition of fractional derivative
About the Authors
Douglas R. Anderson is professor and chair of the mathematics department at Concordia College, Moorhead. His research areas of interest include dynamic equations on time scales and Ulam-type stability of difference and dynamic equations. He is also active in investigating the existence of solutions for boundary value problems.
Svetlin G. Georgiev is currently professor at Sorbonne University, Paris, France and works in various areas of mathematics. He currently focuses on harmonic analysis, partial differential equations, ordinary differential equations, Clifford and quaternion analysis, dynamic calculus on time scales, and integral equations.
Contents
1. Conformable Dynamic Calculus on Time Scales. 2. First Order Linear Dynamic Equations. 3. Conformable Dynamic Systems on Time Scales. 4. Linear Conformable Inequalities. 5. Cauchy Type Problem for a Class Nonlinear Conformable Dynamic Equations. 6. Higher Order Linear Conformable Dynamic Equations with Constant Coefficients. 7. Second Order Conformable Dynamic Equations. 8. Second-Order Self-Adjoint Conformable Dynamic Equations. 9. The Conformable Laplace Transform. Appendix A. Derivatives on Banach Spaces. Appendix B. A Chain Rule.
