Results 21 to 30 of about 125,128 (279)

Multidimensional Time Fractional Diffusion Equation [PDF]

, 2017
In this paper we present integral and series representations for the fundamental solution of the time fractional diffusion equation in an arbitrary dimension. The series representation obtained depends on the parity of the dimension. As an application of our results we study the diffusion and stress in the axially symmetric case for plane deformation ...
Ferreira, Milton dos Santos, Vieira, Nelson Felipe Loureiro   +1 more
openaire   +2 more sources

Homotopy Perturbation ρ-Laplace Transform Method and Its Application to the Fractional Diffusion Equation and the Fractional Diffusion-Reaction Equation

Fractal and Fractional, 2019
In this paper, the approximate solutions of the fractional diffusion equations described by the fractional derivative operator were investigated. The homotopy perturbation Laplace transform method of getting the approximate solution was proposed.
Ndolane Sene, Aliou Niang Fall
doaj   +1 more source

A Galerkin finite element method to solve fractional diffusion and fractional diffusion-wave equations

Mathematical Modelling and Analysis, 2013
In the present study, numerical solutions of the fractional diffusion and fractional diffusion-wave equations where fractional derivatives are considered in the Caputo sense have been obtained by a Galerkin finite element method using quadratic B-spline ...
Alaattin Esen, Yusuf Ucar, Nuri Yagmurlu, Orkun Tasbozan   +3 more
doaj   +1 more source

Numerical solution of fractional diffusion equation by Chebyshev collocation method and residual power series method

Alexandria Engineering Journal, 2020
In this paper, we propose an efficient Chebyshev collocation scheme to solve diffusion problem including time fractional diffusion equation considering the fractional derivative in the Liouville-Caputo sense. By making use of shifted Chebyshev polynomial
Mine Aylin Bayrak, Ali Demir, Ebru Ozbilge   +2 more
doaj   +1 more source

Finite Difference Scheme and Finite Volume Scheme for Fractional Laplacian Operator and Some Applications

Fractal and Fractional, 2023
The fractional Laplacian operator is a very important fractional operator that is often used to describe several anomalous diffusion phenomena. In this paper, we develop some numerical schemes, including a finite difference scheme and finite volume ...
Junjie Wang, Shoucheng Yuan, Xiao Liu
doaj   +1 more source

Linear Boltzmann equation and fractional diffusion

Kinetic & Related Models, 2018
25 pages, no ...
Bardos, Claude, Golse, François, Moyano, Iván   +2 more
openaire   +6 more sources

On a nonlocal analog of the Kuramoto-Sivashinsky equation [PDF]

, 2014
We study a nonlocal equation, analogous to the Kuramoto-Sivashinsky equation, in which short waves are stabilized by a possibly fractional diffusion of order less than or equal to two, and long waves are destabilized by a backward fractional diffusion of
Granero-Belinchón, Rafael, Hunter, John K.   +1 more
core   +2 more sources

A new class of travelling wave solutions for local fractional diffusion differential equations

Advances in Difference Equations, 2020
In this paper, we investigate a 3-D diffusion equation within the scope of the local fractional derivative. For this model, we establish local fractional vector operators and a local fractional Laplace operator defined on Cantor-type cylindrical ...
Ziyue Shi, Wei Qi, Jing Fan
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

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
doaj   +1 more source