# Stochastic interpretation of g-subdiffusion process.

@article{Kosztoowicz2021StochasticIO, title={Stochastic interpretation of g-subdiffusion process.}, author={Tadeusz Kosztołowicz and Aldona Dutkiewicz}, journal={Physical review. E}, year={2021}, volume={104 4}, pages={ L042101 } }

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.

- MathematicsPhysical review. E
- 2021

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

- Mathematics
- 2022

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

- Mathematics
- 2022

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…

## References

SHOWING 1-10 OF 34 REFERENCES

From diffusion to anomalous diffusion: a century after Einstein's Brownian motion.

- MathematicsChaos
- 2005

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.

Subdiffusion in a system consisting of two different media separated by a thin membrane

- Mathematics
- 2015

Why the Mittag-Leffler Function Can Be Considered the Queen Function of the Fractional Calculus?

- MathematicsEntropy
- 2020

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

- PhysicsJanuary 1
- 1986

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…

A Caputo fractional derivative of a function with respect to another function

- MathematicsCommun. Nonlinear Sci. Numer. Simul.
- 2017

Fractional Diffusion Based on Riemann-Liouville Fractional Derivatives †

- Mathematics
- 2000

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

- MathematicsWSEAS TRANSACTIONS ON 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

- Mathematics
- 1989

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

- MathematicsRevista 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…