Variational formulation and optimal control of fractional diffusion equations with Caputo derivatives

DOI10.1186/S13662-015-0593-5zbMath1347.49004OpenAlexW2168757457WikidataQ59434432 ScholiaQ59434432MaRDI QIDQ738484

Qing Tang, Qingxia Ma

Publication date: 2 September 2016

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13662-015-0593-5

zbMATH Keywords

optimal controlvariational formulationfractional diffusion equationfractional Sobolev spacedistributional weak Caputo derivative

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Fractional derivatives and integrals (26A33) Existence theories for optimal control problems involving partial differential equations (49J20) Fractional partial differential equations (35R11) PDEs in connection with control and optimization (35Q93)

Related Items (12)

Optimal Control Problem for Systems Modelled by Diffusion-Wave Equation, ⋮ Optimal Damping Problem for Diffusion-Wave Equation ⋮ Fractional optimal control problem for variable-order differential systems ⋮ Optimal control for systems modeled by the diffusion-wave equation ⋮ Existence, uniqueness and continuation of solution of a sub diffusion functional differential equations with an integral condition ⋮ Iterative methods for mesh approximations of optimal control problems controlled by linear equations with fractional derivatives ⋮ Optimal control problem for coupled time-fractional evolution systems with control constraints ⋮ Galerkin method for time fractional diffusion equations ⋮ Uniqueness and numerical scheme for the Robin coefficient identification of the time-fractional diffusion equation ⋮ Time-optimal boundary control for systems defined by a fractional order diffusion equation ⋮ Global and regional constrained controllability for distributed parabolic linear systems: RHUM approach ⋮ Necessary optimality conditions of a reaction-diffusion SIR model with ABC fractional derivatives

Cites Work

• Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems
• Necessary and sufficient conditions for the fractional calculus of variations with Caputo derivatives
• Sobolev, Besov and Nikolskii fractional spaces: Imbeddings and comparisons for vector valued spaces on an interval
• Compact sets in the space \(L^ p(0,T;B)\)
• Quasilinear evolutionary equations and continuous interpolation spaces.
• Time-fractional diffusion equation in the fractional Sobolev spaces
• Concrete characterization of the domains of fractional powers of some elliptic differential operators of the second order
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