Stochastic interpretation of g-subdiffusion process.

@article{Kosztoowicz2021StochasticIO,
title={Stochastic interpretation of g-subdiffusion process.},
journal={Physical review. E},
year={2021},
volume={104 4},
pages={
L042101
}
}
• Published 22 July 2021
• Mathematics
• Physical review. E
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…
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References

SHOWING 1-10 OF 34 REFERENCES
From diffusion to anomalous diffusion: a century after Einstein's Brownian motion.
• Mathematics
Chaos
• 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.
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
WSEAS 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
• 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