A review on variable-order fractional differential equations: mathematical foundations, physical models, numerical methods and applications
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 …
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 …
recent years. The possibility of formulating evolutionary governing equations has led to the …
[图书][B] Fractional derivative modeling in mechanics and engineering
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 …
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 …
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 …
and author profiles for this publication at: https://www.researchgate.net/publication/275071882 …
Variable-order fractional differential operators in anomalous diffusion modeling
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 …
operators in anomalous diffusion modeling. The characteristics of the new models, in …
Numerical simulation for two-dimensional variable-order fractional nonlinear cable equation
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 …
neuronal dynamics. This paper reports an accurate spectral collocation method for solving …
[图书][B] Fractional Calculus
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 …
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 …
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 …
fractional diffusion equation over an open bounded domain G×(0, T), G∈ Rn are …