Time-fractional diffusion equationConservation lawNonlinear self-adjointnessSymmetryThe concept of nonlinear self-adjointness is employed to construct theconservation laws for fractional evolution equations using its Lie pointsymmetries. The approach is demonstrated on subdiffusion and diffusion-waveequations ...
[10] investigated a variable-order anomalous subdiffusion equation and developed a numerical scheme characterized by first-order temporal and fourth-order spatial accuracy. Concurrently, they employed Fourier analysis techniques to rigorously analyze their numerical scheme’s convergence, stability, and ...
The TFSE corresponds to a ???subdiffusion??? equation with an imaginary fractional diffusion constant and reproduces the regular Schrodinger equation in the limit of integer order. The present work corrects a number of errors in Naber???s work. The correct continuity equation for the probability...
SUBDIFFUSION EQUATIONSCALCULUSWe consider the homogeneous time-fractional diffusion equation partial derivative(alpha) (u - u(0)) (t) + Au(t) = 0, t ... M Achache - 《Zeitschrift Fur Analysis Und Ihre Anwendungen》 被引量: 0发表: 2023年 A NON-LINEAR STABLE NON-GAUSSIAN PROCESS IN FRACT...
Modelling, analysis, and numerical methods for a geometric inverse source problem in variable-order time-fractional subdiffusion There exist research works on studying time-dependent integer-order and time-fractional constant-order geometric inverse source problems in the literature... W Fan,X Hu,S Zh...
Finite variance waiting times lead to a second-order partial differential equation in time. In this article we investigate the various solutions with regard to moment growth and scaling properties, and show that even infinite mean waiting times do not necessarily induce subdiffusion, but can lead ...
An algorithm which solves the multidimensional diffusion equation on complex shapes to fourth-order accuracy and is asymptotically stable in time is presen... S Abarbanel,A Ditkowski - Academic Press Professional, Inc. 被引量: 82发表: 1997年 Estimation of parameters in fractional subdiffusion equati...
This article is concerned with a semilinear time-fractional diffusion equation with a superlinear convex semilinear term in a bounded domain Ω \Omega with the homogeneous Dirichlet, Neumann, Robin boundary conditions and non-negative and not identically vanishing initial value. The order of the fracti...
We prove optimal estimates for the decay in time of solutions to a rather general class of non-local in time subdiffusion equations in \\(\\mathbb {R}^d\\). An important special case is the time-fractional diffusion equation, which has seen much interest during the last years, mostly ...
In this work, we consider a time-fractional Allen–Cahn equation, where the conventional first order time derivative is replaced by a Caputo fractional derivative with order α∈(0,1). First, the well-posedness and (limited) smoothing property are studied, by using the maximal Lp regularity of...