Variable-order porous media equations: Application on modeling the S&P500 and Bitcoin price return
Y Tang, F Gharari, K Arias-Calluari… - Physical Review E, 2024 - APS
This article reveals a specific category of solutions for the 1+ 1 variable order (VO) nonlinear
fractional Fokker-Planck equations. These solutions are formulated using VO q-Gaussian …
fractional Fokker-Planck equations. These solutions are formulated using VO q-Gaussian …
Particle invasion, survival, and non-ergodicity in 2D diffusion processes with space-dependent diffusivity
We study the thermal Markovian diffusion of tracer particles in a 2D medium with spatially
varying diffusivity D (r), mimicking recently measured, heterogeneous maps of the apparent …
varying diffusivity D (r), mimicking recently measured, heterogeneous maps of the apparent …
Fractional and fractal derivative models for transient anomalous diffusion: Model comparison
Transient anomalous diffusion characterized by transition between diffusive states (ie, sub-
diffusion and normal-diffusion) is not uncommon in real-world geologic media, due to the …
diffusion and normal-diffusion) is not uncommon in real-world geologic media, due to the …
On time-fractional diffusion equations with space-dependent variable order
Y Kian, E Soccorsi, M Yamamoto - Annales Henri Poincaré, 2018 - Springer
This paper deals with mathematical problems related to space-dependent anomalous
diffusion processes. Namely, we investigate diffusion equations with time-fractional …
diffusion processes. Namely, we investigate diffusion equations with time-fractional …
Analytical and numerical treatment of continuous ageing in the voter model
The conventional voter model is modified so that an agent's switching rate depends on the
'age'of the agent—that is, the time since the agent last switched opinion. In contrast to …
'age'of the agent—that is, the time since the agent last switched opinion. In contrast to …
Existence of a unique weak solution to a non-autonomous time-fractional diffusion equation with space-dependent variable order
K Van Bockstal - Advances in Difference Equations, 2021 - Springer
In this contribution, we investigate an initial-boundary value problem for a fractional diffusion
equation with Caputo fractional derivative of space-dependent variable order where the …
equation with Caputo fractional derivative of space-dependent variable order where the …
Continuous time random walks with reactions forcing and trapping
One of the central results in Einstein's theory of Brownian motion is that the mean square
displacement of a randomly moving Brownian particle scales linearly with time. Over the …
displacement of a randomly moving Brownian particle scales linearly with time. Over the …
Data-driven modelling of drug tissue trapping using anomalous kinetics
This work revisits the pharmacokinetic models derived from classical differential equations
and proposes an extension to fractional differential equations to account for tissue trapping …
and proposes an extension to fractional differential equations to account for tissue trapping …
On time‐fractional partial differential equations of time‐dependent piecewise constant order
Y Kian, M Slodička, É Soccorsi… - … Methods in the …, 2024 - Wiley Online Library
This contribution considers the time‐fractional subdiffusion with a time‐dependent variable‐
order fractional operator of order β (t) β (t). It is assumed that β (t) β (t) is a piecewise …
order fractional operator of order β (t) β (t). It is assumed that β (t) β (t) is a piecewise …
Asymptotic behavior of the solution of the space dependent variable order fractional diffusion equation: Ultraslow anomalous aggregation
We find the asymptotic representation of the solution of the variable-order fractional diffusion
equation, which remains unsolved since it was proposed by Chechkin, Gorenflo, and …
equation, which remains unsolved since it was proposed by Chechkin, Gorenflo, and …