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.
