Numerical methods for time-fractional evolution equations with nonsmooth data: a concise overview
Over the past few decades, there has been substantial interest in evolution equations that
involve a fractional-order derivative of order α∈(0, 1) in time, commonly known as …
involve a fractional-order derivative of order α∈(0, 1) in time, commonly known as …
fPINNs: Fractional physics-informed neural networks
Physics-informed neural networks (PINNs), introduced in M. Raissi, P. Perdikaris, and G.
Karniadakis, J. Comput. Phys., 378 (2019), pp. 686--707, are effective in solving integer …
Karniadakis, J. Comput. Phys., 378 (2019), pp. 686--707, are effective in solving integer …
[HTML][HTML] Fractional order modelling of omicron SARS-CoV-2 variant containing heart attack effect using real data from the United Kingdom
In this study, a new approach to COVID-19 pandemic is presented. In this context, a
fractional order pandemic model is developed to examine the spread of COVID-19 with and …
fractional order pandemic model is developed to examine the spread of COVID-19 with and …
Error analysis of a finite difference method on graded meshes for a time-fractional diffusion equation
A reaction-diffusion problem with a Caputo time derivative of order α∈(0,1) is considered.
The solution of such a problem is shown in general to have a weak singularity near the initial …
The solution of such a problem is shown in general to have a weak singularity near the initial …
Investigation of interactions between COVID-19 and diabetes with hereditary traits using real data: A case study in Turkey
In the present paper, interactions between COVID-19 and diabetes are investigated using
real data from Turkey. Firstly, a fractional order pandemic model is developed both to …
real data from Turkey. Firstly, a fractional order pandemic model is developed both to …
Sharp error estimate of the nonuniform L1 formula for linear reaction-subdiffusion equations
Stability and convergence of the L1 formula on nonuniform time grids are studied for solving
linear reaction-subdiffusion equations with the Caputo derivative. A discrete fractional …
linear reaction-subdiffusion equations with the Caputo derivative. A discrete fractional …
A discrete Gronwall inequality with applications to numerical schemes for subdiffusion problems
We consider a class of numerical approximations to the Caputo fractional derivative. Our
assumptions permit the use of nonuniform time steps, such as is appropriate for accurately …
assumptions permit the use of nonuniform time steps, such as is appropriate for accurately …
[KIRJA][B] Fractional differential equations
B ** - 2021 - Springer
Fractional differential equations (FDES), ie, differential equations involving fractional-order
derivatives, have received much recent attention in engineering, physics, biology and …
derivatives, have received much recent attention in engineering, physics, biology and …
Error analysis of the L1 method on graded and uniform meshes for a fractional-derivative problem in two and three dimensions
N Kopteva - Mathematics of Computation, 2019 - ams.org
An initial-boundary value problem with a Caputo time derivative of fractional order $\alpha\in
(0, 1) $ is considered, solutions of which typically exhibit a singular behaviour at an initial …
(0, 1) $ is considered, solutions of which typically exhibit a singular behaviour at an initial …
Numerical analysis of nonlinear subdiffusion equations
We present a general framework for the rigorous numerical analysis of time-fractional
nonlinear parabolic partial differential equations, with a fractional derivative of order α∈(0,1) …
nonlinear parabolic partial differential equations, with a fractional derivative of order α∈(0,1) …