A review on variable-order fractional differential equations: mathematical foundations, physical models, numerical methods and applications

HG Sun, A Chang, Y Zhang, W Chen - Fractional Calculus and …, 2019 - degruyter.com
Variable-order (VO) fractional differential equations (FDEs) with a time (t), space (x) or other
variables dependent order have been successfully applied to investigate time and/or space …

[BOOK][B] Mittag-Leffler functions, related topics and applications

R Gorenflo, AA Kilbas, F Mainardi, SV Rogosin - 2020 - Springer
Mittag-Leffler Functions, Related Topics and Applications Page 1 Springer Monographs in
Mathematics Rudolf Gorenflo Anatoly A. Kilbas Francesco Mainardi Sergei Rogosin Mittag-Leffler …

[BOOK][B] Fractional-order nonlinear systems: modeling, analysis and simulation

I Petráš - 2011 - books.google.com
" Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation" presents a study
of fractional-order chaotic systems accompanied by Matlab programs for simulating their …

Finite difference methods for fractional differential equations

C Li, F Zeng - International Journal of Bifurcation and Chaos, 2012 - World Scientific
In this review paper, the finite difference methods (FDMs) for the fractional differential
equations are displayed. The considered equations mainly include the fractional kinetic …

[BOOK][B] Fractional derivatives for physicists and engineers

VV Uchaikin - 2013 - Springer
“God made the integers; all else is the work of man” 1. For centuries, the ancients were
satisfied with using natural numbers called simply “numbers”. What we call irrational …

[BOOK][B] Fractional order systems: modeling and control applications

R Caponetto, G Dongola, L Fortuna, I Petras - 2010 - books.google.com
This book aims to propose the implementation and application of Fractional Order Systems
(FOS). It is well known that FOS can be utilized in control applications and systems …

[BOOK][B] Fractional derivative modeling in mechanics and engineering

W Chen, HG Sun, X Li - 2022 - Springer
Classic Newtonian mechanics assumes that space and time are continuous everywhere.
The basic physical quantities (eg speed, acceleration and force) can be described by an …

[HTML][HTML] Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions

B Ahmad, JJ Nieto - Computers & Mathematics with Applications, 2009 - Elsevier
Existence results for a coupled system of nonlinear fractional differential equations with
three-point boundary conditions - ScienceDirect Skip to main contentSkip to article Elsevier logo …

Finite element method for the space and time fractional Fokker–Planck equation

W Deng - SIAM journal on numerical analysis, 2009 - SIAM
We develop the finite element method for the numerical resolution of the space and time
fractional Fokker–Planck equation, which is an effective tool for describing a process with …

[BOOK][B] Fractional operators with constant and variable order with application to geo-hydrology

A Atangana - 2017 - books.google.com
Fractional Operators with Constant and Variable Order with Application to Geo-hydrology
provides a physical review of fractional operators, fractional variable order operators, and …