Addresses the rapidly growing -field of fractional calculus and
provides simpli-fied solutions for linear commensurate-order fractional
differential equations
-The Fractional Trigonometry: With Applications to Fractional
Differential Equations and Science is the result of the authors' work
in fractional calculus, and more particularly, in functions for the
solutions of fractional di-fferential equations, which is fostered in
the behavior of generalized exponential functions. The authors discuss
how fractional trigonometry plays a role analogous to the classical
trigonometry for the fractional calculus by providing solutions to
linear fractional di-fferential equations. The book begins with an
introductory chapter that o-ffers insight into the fundamentals of
fractional calculus, and topical coverage is then organized in two main
parts. Part One develops the definitions and theories of fractional
exponentials and fractional trigonometry. Part Two provides insight into
various areas of potential application within the sciences. The
fractional exponential function via the fundamental fractional
differential equation, the generalized exponential function, and
R-function relationships are discussed in addition to the fractional
hyperboletry, the R1-fractional trigonometry, the R2-fractional
trigonometry, and the R3-trigonometric functions. -The Fractional
Trigonometry: With Applications to Fractional Differential Equations and
Science also:
- Presents fractional trigonometry as a tool for scientists and
engineers and discusses how to apply fractional-order methods to the
current toolbox of mathematical modelers
- Employs a mathematically clear presentation in an e- ort to make the
topic broadly accessible
- Includes solutions to linear fractional di-fferential equations and
generously features graphical forms of functions to help readers
visualize the presented concepts
- Provides e-ffective and efficient methods to describe complex
structures
-The Fractional Trigonometry: With Applications to Fractional
Differential Equations and Science is an ideal reference for academic
researchers, research engineers, research scientists, mathematicians,
physicists, biologists, and chemists who need to apply new fractional
calculus methods to a variety of disciplines. The book is also
appropriate as a textbook for graduate- and PhD-level courses in
fractional calculus.
Carl F. Lorenzo is Distinguished Research Associate at the NASA
Glenn Research Center in Cleveland, Ohio. His past positions include
chief engineer of the Instrumentation and Controls Division and chief of
the Advanced Controls Technology and Systems Dynamics branches at NASA.
He is internationally recognized for his work in the development and
application of the fractional calculus and fractional trigonometry.
Tom T. Hartley, PhD, is Emeritus Professor in the Department of
Electrical and Computer Engineering at The University of Akron. Dr
Hartley is a recognized expert in fractional-order systems, and together
with Carl Lorenzo, has solved fundamental problems in the area including
Riemann's complementary-function initialization function problem. He
received his PhD in Electrical Engineering from Vanderbilt University.
