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 …
[图书][B] Fractional calculus with applications in mechanics: vibrations and diffusion processes
This book contains mathematical preliminaries in which basic definitions of fractional
derivatives and spaces are presented. The central part of the book contains various …
derivatives and spaces are presented. The central part of the book contains various …
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
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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 …
Second-order approximations for variable order fractional derivatives: algorithms and applications
X Zhao, Z Sun, GE Karniadakis - Journal of Computational Physics, 2015 - Elsevier
Fractional calculus allows variable-order of fractional operators, which can be exploited in
diverse physical and biological applications where rates of change of the quantity of interest …
diverse physical and biological applications where rates of change of the quantity of interest …
[图书][B] Fractional calculus with applications in mechanics: wave propagation, impact and variational principles
The books Fractional Calculus with Applications in Mechanics: Vibrations and Diffusion
Processes and Fractional Calculus with Applications in Mechanics: Wave Propagation …
Processes and Fractional Calculus with Applications in Mechanics: Wave Propagation …
Numerical techniques for the variable order time fractional diffusion equation
In this paper we consider the variable order time fractional diffusion equation. We adopt the
Coimbra variable order (VO) time fractional operator, which defines a consistent method for …
Coimbra variable order (VO) time fractional operator, which defines a consistent method for …
[图书][B] Computational methods in the fractional calculus of variations
This book fills a gap in the literature by introducing numerical techniques to solve problems
of fractional calculus of variations (FCV). In most cases, finding the analytic solution to such …
of fractional calculus of variations (FCV). In most cases, finding the analytic solution to such …