Stochastic interpretation of g-subdiffusion process.

  title={Stochastic interpretation of g-subdiffusion process.},
  author={Tadeusz Kosztołowicz and Aldona Dutkiewicz},
  journal={Physical review. E},
  volume={104 4},
Recently, we considered the g-subdiffusion equation with a fractional Caputo time derivative with respect to another function g, T. Kosztołowicz et al. [Phys. Rev. E 104, 014118 (2021)2470-004510.1103/PhysRevE.104.014118]. This equation offers different possibilities for modeling diffusion such as a process in which a type of diffusion evolves continuously over time. However, the equation has not been derived from a stochastic model and the stochastic interpretation of g subdiffusion is still… 
3 Citations
Subdiffusion equation with Caputo fractional derivative with respect to another function.
An application of a subdiffusion equation with Caputo fractional time derivative with respect to another function g to describe subDiffusion in a medium having a structure evolving over time to consider the transition from "ordinary" subdiffusions to ultraslow diffusion.
$G$-subdiffusion equation that describes transient subdiffusion
A g –subdiffusion equation with fractional Caputo time derivative with respect to another function g is used to describe a process of a continuous transition from subdiffusion with parameters α and D α
First passage time for $g$--subdiffusion process of vanishing particles
Subdiffusion equation and molecule survival equation, both with Caputo fractional time derivatives with respect to another functions g1 and g2, respectively, are used to describe diffusion of a


From diffusion to anomalous diffusion: a century after Einstein's Brownian motion.
Two different but equivalent forms of kinetic equations, which reduce to known fractional diffusion or Fokker-Planck equations for waiting-time distributions following a power law, are derived.
Why the Mittag-Leffler Function Can Be Considered the Queen Function of the Fractional Calculus?
This survey stresses the importance of the higher transcendental Mittag-Leffler function in the framework of the Fractional Calculus and sketches some historical aspects related to the author’s acquaintance with this function.
The Realization of the Generalized Transfer Equation in a Medium with Fractal Geometry
It is shown that in a medium representing an example of “Koch's tree”-type fractional structure the diffusion process is described by a generalized transfer equation in partial derivations. Such a
Fractional Diffusion Based on Riemann-Liouville Fractional Derivatives †
A fractional diffusion equation based on Riemann−Liouville fractional derivatives is solved exactly. The initial values are given as fractional integrals. The solution is obtained in terms of
A Tutorial on the Basic Special Functions of Fractional Calculus
  • F. Mainardi
  • Mathematics
  • 2020
In this tutorial survey we recall the basic properties of the special function of the Mittag-Leffler and Wright type that are known to be relevant in processes dealt with the fractional calculus. We
Fractional diffusion and wave equations
Diffusion and wave equations together with appropriate initial condition(s) are rewritten as integrodifferential equations with time derivatives replaced by convolution with tα−1/Γ(α), α=1,2,
On $$\psi $$ψ-Caputo time fractional diffusion equations: extremum principles, uniqueness and continuity with respect to the initial data
  • B. SametYong Zhou
  • Mathematics
    Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
  • 2019
Estimates of the $$\psi $$ψ-Caputo fractional derivative of order $$0<\alpha <1$$0<α<1 of a function at its extreme points are obtained; they are used to derive extremum principles for a linear