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Erdélyi-Kober fractional diffusion [PDF]

Fractional Calculus and Applied Analysis, 2011
The aim of this Short Note is to highlight that the {\it generalized grey Brownian motion} (ggBm) is an anomalous diffusion process driven by a fractional integral equation in the sense of Erdélyi-Kober, and for this reason here it is proposed to call such family of diffusive processes as {\it Erdélyi-Kober fractional diffusion}.
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Analysis of the fractional diffusion equations with fractional derivative of non-singular kernel

Advances in Difference Equations, 2017
In this paper we study linear and nonlinear fractional diffusion equations with the Caputo fractional derivative of non-singular kernel that has been launched recently (Caputo and Fabrizio in Prog. Fract. Differ. Appl. 1(2):73-85, 2015).
Mohammed Al-Refai, Thabet Abdeljawad
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Fractional Reaction-Diffusion Equations [PDF]

Astrophysics and Space Science, 2006
LaTeX, 17 pages, corrected ...
Saxena, R. K., Mathai, A. M., Haubold, H. J.   +2 more
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Solutions of Fractional Diffusion Equations and Cattaneo-Hristov Diffusion Model

International Journal of Analysis and Applications, 2019
The analytical solutions of the fractional diffusion equations in one and two-dimensional spaces have been proposed. The analytical solution of the Cattaneo-Hristov diffusion model with the particular boundary conditions has been suggested.
Ndolane Sene
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Simultaneous determination of a source term and diffusion concentration for a multi-term space-time fractional diffusion equation

Mathematical Modelling and Analysis, 2021
An inverse problem of determining a time dependent source term along with diffusion/temperature concentration from a non-local over-specified condition for a space-time fractional diffusion equation is considered.
Salman A. Malik, Asim Ilyas, Arifa Samreen   +2 more
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The Role of Fractional Time-Derivative Operators on Anomalous Diffusion

Frontiers in Physics, 2017
The generalized diffusion equations with fractional order derivatives have shown be quite efficient to describe the diffusion in complex systems, with the advantage of producing exact expressions for the underlying diffusive properties.
Angel A. Tateishi, Haroldo V. Ribeiro, Ervin K. Lenzi   +2 more
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Supplement a high-dimensional time fractional diffusion equation

Alexandria Engineering Journal, 2023
In this article, we discussed a high-dimensional time fractional diffusion equation which is used to write many nonlinear phenomena in three dimensional space diffusion processes.
Jian-Gen Liu, Fa-Zhan Geng, Xin Li
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Applications of the Fractional Calculus: On a Discretization of Fractional Diffusion Equation in One Dimension

Communications, 2010
The paper discusses the problem of classical and fractional diffusion models. It is known that the classical model fails in heterogeneous structures with locations where particles move at a large speed over a long distance.
Tomas Kisela
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Modeling Long-Distance Forward and Backward Diffusion Processes in Tracer Transport Using the Fractional Laplacian on Bounded Domains

Fractal and Fractional, 2023
Recent studies have emphasized the importance of the long-distance diffusion model in characterizing tracer transport occurring within both subsurface and surface environments, particularly in heterogeneous systems.
Zhipeng Li, Hongwu Tang, Saiyu Yuan, Huiming Zhang, Lingzhong Kong, HongGuang Sun   +5 more
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Fractional Advection-Diffusion-Asymmetry Equation [PDF]

Physical Review Letters, 2020
Fractional kinetic equations employ non-integer calculus to model anomalous relaxation and diffusion in many systems. While this approach is well explored, it so far failed to describe an important class of transport in disordered systems. Motivated by work on contaminant spreading in geological formations we propose and investigate a fractional ...
Wanli Wang, Eli Barkai
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