Results 31 to 40 of about 17,486 (265)

Solutions of the Fractional Reaction Equation and the Fractional Diffusion Equation [PDF]

, 2009
In view of the role of reaction equations in physical problems, the authors derive the explicit solution of a fractional reaction equation of general character, that unifies and extends earlier results. Further, an alternative shorter method based on a result developed by the authors is given to derive the solution of a fractional diffusion equation ...
Saxena, R. K., Mathai, A. M., Haubold, H. J.   +2 more
openaire   +2 more sources

Analytical Solutions of the Diffusion–Wave Equation of Groundwater Flow with Distributed-Order of Atangana–Baleanu Fractional Derivative

Applied Sciences, 2021
A generalized mathematical model of the radial groundwater flow to or from a well is studied using the time-fractional derivative with Mittag-Lefler kernel.
Nehad Ali Shah, Abdul Rauf, Dumitru Vieru, Kanokwan Sitthithakerngkiet, Poom Kumam   +4 more
doaj   +1 more source

Fractional Diffusion Models for the Atmosphere of Mars

Fractal and Fractional, 2017
The dust aerosols floating in the atmosphere of Mars cause an attenuation of the solar radiation traversing the atmosphere that cannot be modeled through the use of classical diffusion processes.
Salvador Jiménez, David Usero, Luis Vázquez, Maria Pilar Velasco   +3 more
doaj   +1 more source

Numeric Fem’s Solution for Space-Time Diffusion Partial Differential Equations with Caputo–Fabrizion and Riemann–Liouville Fractional Order’s Derivatives

Annales Mathematicae Silesianae, 2023
In this paper, we use the finite element method to solve the fractional space-time diffusion equation over finite fields. This equation is obtained from the standard diffusion equation by replacing the first temporal derivative with the new fractional ...
Boutiba Malika, Baghli-Bendimerad Selma, Fečkan Michal   +2 more
doaj   +1 more source

Cauchy problem for nonlocal diffusion equations modelling Lévy flights

Electronic Journal of Qualitative Theory of Differential Equations, 2022
In the present paper, we study the time-space fractional diffusion equation involving the Caputo differential operator and the fractional Laplacian. This equation describes the Lévy flight with the Brownian motion component and the drift component. First,
Chung-Sik Sin
doaj   +1 more source

Lattice Boltzmann Simulation of Spatial Fractional Convection–Diffusion Equation

Entropy
The space fractional advection–diffusion equation is a crucial type of fractional partial differential equation, widely used for its ability to more accurately describe natural phenomena. Due to the complexity of analytical approaches, this paper focuses
Xiaohua Bi, Huimin Wang
doaj   +1 more source

On a Fractional Master Equation

International Journal of Differential Equations, 2011
A fractional order time-independent form of the wave equation or diffusion equation in two dimensions is obtained from the standard time-independent form of the wave equation or diffusion equation in two-dimensions by replacing the integer order partial ...
Anitha Thomas
doaj   +1 more source

An approximate group classification of a perturbed subdiffusion equation

Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2016
A problem of the Lie point approximate symmetry group classification of a perturbed subdiffusion equation with a small parameter is solved. The classification is performed with respect to anomalous diffusion coefficient which is considered as a function ...
Stanislav Yu Lukashchuk
doaj   +1 more source

A scalable framework for solving fractional diffusion equations [PDF]

Proceedings of the 34th ACM International Conference on Supercomputing, 2020
The study of fractional order differential operators is receiving renewed attention in many scientific fields. In order to accommodate researchers doing work in these areas, there is a need for highly scalable numerical methods for solving partial differential equations that involve fractional order operators on complex geometries. These operators have
Max Carlson, Robert M. Kirby, Hari Sundar   +2 more
openaire   +2 more sources

Algorithms for numerical solving of 2D anomalous diffusion problems

Mathematical Modelling and Analysis, 2012
Fractional analog of the reaction diffusion equation is used to model the subdiffusion process. Diffusion equation with fractional Riemann–Liouville operator is analyzed in this paper.
Natalia Abrashina-Zhadaeva, Natalie Romanova   +1 more
doaj   +1 more source