Fractional diffusion equation with distributed-order Caputo derivative

DOI10.1216/JIE-2019-31-2-195zbMath1423.35427arXiv1706.05591MaRDI QIDQ2329287

Adam Kubica, Katarzyna Ryszewska

Publication date: 17 October 2019

Published in: Journal of Integral Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.05591

zbMATH Keywords

weak solutionscontinuity at initial time.distributed-order fractional diffusion

Mathematics Subject Classification ID

Initial value problems for second-order parabolic systems (35K45) Fuzzy partial differential equations (35R13)

Related Items (13)

The well-posedness analysis of distributed order fractional diffusion problems on \(\mathbb{R}^N\) ⋮ The analysis of approximate controllability for distributed order fractional diffusion problems ⋮ Solving a backward problem for a distributed-order time fractional diffusion equation by a new adjoint technique ⋮ The well-posedness for the distributed-order wave equation on \(\mathbb{R}^N\) ⋮ Qualitative analysis of solutions to mixed-order positive linear coupled systems with bounded or unbounded delays ⋮ Fractional Stefan problem: a survey of the recent results ⋮ Equivalence of definitions of solutions for some class of fractional diffusion equations ⋮ Explicit solutions to fractional Stefan-like problems for Caputo and Riemann-Liouville derivatives ⋮ Existence and uniqueness of a weak solution to a non-autonomous time-fractional diffusion equation (of distributed order) ⋮ Recovering the weight function in distributed order fractional equation from interior measurement ⋮ On Viscosity Solutions of Space-Fractional Diffusion Equations of Caputo Type ⋮ Initial-boundary value problems for multi-term time-fractional diffusion equations with \(x \)-dependent coefficients ⋮ An inverse source problem for distributed order time-fractional diffusion equation

Cites Work

• Unnamed Item
• Unnamed Item
• Analysis of fractional diffusion equations of distributed order: maximum principles and their applications
• General fractional calculus, evolution equations, and renewal processes
• Weak solutions of fractional differential equations in non cylindrical domains
• Analyticity of solutions to a distributed order time-fractional diffusion equation and its application to an inverse problem
• Initial-boundary value problems for fractional diffusion equations with time-dependent coefficients
• The inverse Laplace transform of some analytic functions with an application to the eternal solutions of the Boltzmann equation
• Asymptotic estimates of solutions to initial-boundary-value problems for distributed order time-fractional diffusion equations
• Distributed order calculus and equations of ultraslow diffusion
• General time-fractional diffusion equation: some uniqueness and existence results for the initial-boundary-value problems
• Fractional diffusion: recovering the distributed fractional derivative from overposed data
• Distributed-order calculus: An operator-theoretic interpretation
• Weak Solutions of Abstract Evolutionary Integro-Differential Equations in Hilbert Spaces
• Completely monotone functions and some classes of fractional evolution equations

This page was built for publication: Fractional diffusion equation with distributed-order Caputo derivative