Open AccessBook
Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering
Jocelyn Sabatier,Om P. Agrawal,J. A. Tenreiro Machado +2 more
- pp 552
Reads0
Chats0
TLDR
In the last two decades, fractional differentiation has played a very important role in various fields such as mechanics, electricity, chemistry, biology, economics, control theory and signal and image processing as discussed by the authors.Abstract:
In the last two decades, fractional (or non integer) differentiation has played a very important role in various fields such as mechanics, electricity, chemistry, biology, economics, control theory and signal and image processing. For example, in the last three fields, some important considerations such as modelling, curve fitting, filtering, pattern recognition, edge detection, identification, stability, controllability, observability and robustness are now linked to long-range dependence phenomena. Similar progress has been made in other fields listed here. The scope of the book is thus to present the state of the art in the study of fractional systems and the application of fractional differentiation. As this volume covers recent applications of fractional calculus, it will be of interest to engineers, scientists, and applied mathematicians.read more
Citations
More filters
Journal ArticleDOI
Technical communique: Mittag-Leffler stability of fractional order nonlinear dynamic systems
TL;DR: The definition of Mittag-Leffler stability is proposed and the fractional Lyapunov direct method is introduced and the application of Riemann-Liouville fractional order systems is extended by using Caputo fractional orders systems.
Journal ArticleDOI
Recent history of fractional calculus
TL;DR: A survey of the major documents and events in the area of fractional calculus that took place since 1974 up to the present date can be found in this article, where the authors report some of the most important documents and major events.
Journal ArticleDOI
Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability
TL;DR: The decaying speed of the Lyapunov function can be more generally characterized which include the exponential stability and power-law stability as special cases.
Book ChapterDOI
Multi-index Mittag-Leffler Functions
TL;DR: In this paper, Dzherbashian [Dzh60] defined a function with positive α 1 > 0, α 2 > 0 and real α 1, β 2, β 3, β 4, β 5, β 6, β 7, β 8, β 9, β 10, β 11, β 12, β 13, β 14, β 15, β 16, β 17, β 18, β 20, β 21, β 22, β 24
Journal ArticleDOI
Global Mittag-Leffler stability and synchronization of memristor-based fractional-order neural networks
TL;DR: The present paper introduces memristor-based fractional-order neural networks and establishes the conditions on the global Mittag-Leffler stability and synchronization are established by using Lyapunov method.