Time-fractional diffusion equation in the fractional Sobolev spaces
type: Item
instance of: scholarly article
title: Time-fractional diffusion equation in the fractional Sobolev spaces
zbMATH Open document ID: 1499.35642
author: Yuri Luchko
author: M. Yamamoto
author: Rudolf Gorenflo
publication date: 2015-06-01T00:00:00Z
Mathematics Subject Classification ID: 35R11
Mathematics Subject Classification ID: 26A33
Mathematics Subject Classification ID: 35C05
Mathematics Subject Classification ID: 35E05
Mathematics Subject Classification ID: 35L05
Mathematics Subject Classification ID: 45K05
Mathematics Subject Classification ID: 60E99
zbMATH DE Number: 6441513
zbMATH Keywords: Riemann-Liouville integral
zbMATH Keywords: Caputo fractional derivative
zbMATH Keywords: fractional Sobolev spaces
zbMATH Keywords: norm equivalences
zbMATH Keywords: fractional diffusion equation in Sobolev spaces
zbMATH Keywords: norm estimates of the solutions
zbMATH Keywords: initial boundary-value problems
zbMATH Keywords: weak solution
zbMATH Keywords: existence and uniqueness results
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1515/fca-2015-0048
OpenAlex ID: W2561023977
cites work: Fractional evolution equations in Banach spaces
cites work: Regularity and Unique Existence of Solution to Linear Diffusion Equation with Multiple Time-Fractional Derivatives
cites work: The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
cites work: Variational formulation for the stationary fractional advection dispersion equation
cites work: Concrete characterization of the domains of fractional powers of some elliptic differential operators of the second order
cites work: Abel integral equations. Analysis and applications
cites work: Operator theoretic treatment of linear Abel integral equations of first kind
cites work: Mittag-Leffler Functions, Related Topics and Applications
cites work: Geometric theory of semilinear parabolic equations
cites work: Variational formulation of problems involving fractional order differential operators
cites work: Q5699297
cites work: Asymptotic estimates of solutions to initial-boundary-value problems for distributed order time-fractional diffusion equations
cites work: Q5634306
cites work: Maximum principle for the generalized time-fractional diffusion equation
cites work: Some uniqueness and existence results for the initial-boundary-value problems for the generalized time-fractional diffusion equation
cites work: Maximum principle and its application for the time-fractional diffusion equations
cites work: Initial-boundary-value problems for the one-dimensional time-fractional diffusion equation
cites work: An operational method for solving fractional differential equations with the Caputo derivatives
cites work: Semigroups of linear operators and applications to partial differential equations
cites work: Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
cites work: Evolutionary Integral Equations and Applications
cites work: Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems
cites work: Q3141895
cites work: Q3207428
cites work: Maximal regularity of type \(L_p\) for abstract parabolic Volterra equations
cites work: Weak Solutions of Abstract Evolutionary Integro-Differential Equations in Hilbert Spaces
DOI: 10.1515/FCA-2015-0048
published in: Fractional Calculus \ Applied Analysis
description: scientific article