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 …

Applications of variable-order fractional operators: a review

S Patnaik, JP Hollkamp… - Proceedings of the …, 2020 - royalsocietypublishing.org
Variable-order fractional operators were conceived and mathematically formalized only in
recent years. The possibility of formulating evolutionary governing equations has led to the …

[图书][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 …

New fractional derivatives with nonlocal and non-singular kernel: theory and application to heat transfer model

A Atangana, D Baleanu - arXiv preprint arXiv:1602.03408, 2016 - arxiv.org
NEW FRACTIONAL DERIVATIVES WITH NONLOCAL AND NON-SINGULAR KERNEL:
THEORY AND APPLICATION TO HEAT TRANSFER MODEL Abdon Atangana a Page 1 …

[PDF][PDF] A review of definitions for fractional derivatives and integral

EC Oliveira, JA Machado - Mathematical Problems in Engineering, 2014 - recipp.ipp.pt
A Review of Definitions for Fractional Derivatives and Integral Page 1 See discussions, stats,
and author profiles for this publication at: https://www.researchgate.net/publication/275071882 …

Variable-order fractional differential operators in anomalous diffusion modeling

HG Sun, W Chen, YQ Chen - Physica A: Statistical Mechanics and its …, 2009 - Elsevier
The purpose of this paper is to offer a unified discussion of variable-order differential
operators in anomalous diffusion modeling. The characteristics of the new models, in …

Numerical simulation for two-dimensional variable-order fractional nonlinear cable equation

AH Bhrawy, MA Zaky - Nonlinear Dynamics, 2015 - Springer
The cable equation plays a central role in many areas of electrophysiology and in modeling
neuronal dynamics. This paper reports an accurate spectral collocation method for solving …

[图书][B] Fractional Calculus

AB Malinowska, T Odzijewicz, DFM Torres… - 2015 - Springer
Fractional Calculus | SpringerLink Skip to main content Advertisement SpringerLink Account
Menu Find a journal Publish with us Track your research Search Cart Book cover Advanced …

A note on fractional order derivatives and table of fractional derivatives of some special functions

A Atangana, A Secer - Abstract and applied analysis, 2013 - Wiley Online Library
The purpose of this note is to present the different fractional order derivatives definition that
are commonly used in the literature on one hand and to present a table of fractional order …

Initial-boundary-value problems for the generalized multi-term time-fractional diffusion equation

Y Luchko - Journal of Mathematical Analysis and Applications, 2011 - Elsevier
In this paper, the initial-boundary-value problems for the generalized multi-term time-
fractional diffusion equation over an open bounded domain G×(0, T), G∈ Rn are …