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, named "fractional conformable derivative", is 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 this first time. As a result, the book is intended for researchers who work on dynamic calculus on time scales and its applications.
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.