Maximum principles for a time-space fractional diffusion equation

DOI10.1016/j.aml.2016.06.010zbMath1350.35044arXiv1605.00836OpenAlexW2963929429MaRDI QIDQ311698

Junxiong Jia, Kexue Li

Publication date: 13 September 2016

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.00836

zbMATH Keywords

fractional derivatives and integralsfull fractional diffusion equation

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Maximum principles in context of PDEs (35B50) Fractional partial differential equations (35R11)

Related Items (16)

Landweber iterative method for identifying the initial value problem of the time-space fractional diffusion-wave equation ⋮ Landweber iterative method for an inverse source problem of time-space fractional diffusion-wave equation ⋮ Global existence, local existence and blow-up of mild solutions for abstract time-space fractional diffusion equations ⋮ Well-posedness for a nonlocal nonlinear diffusion equation and applications to inverse problems ⋮ Maximum principle for the space-time fractional conformable differential system involving the fractional Laplace operator ⋮ Harnack's inequality for a space-time fractional diffusion equation and applications to an inverse source problem ⋮ Space-time spectral method for the Cattaneo equation with time fractional derivative ⋮ \(S\)-asymptotically periodic solutions for time-space fractional evolution equation ⋮ Global existence and blow-up for a space and time nonlocal reaction-diffusion equation ⋮ Maximum principle for space and time-space fractional partial differential equations ⋮ Reconstruction of the temporal component in the source term of a (time-fractional) diffusion equation ⋮ Monotone iterative technique for time-space fractional diffusion equations involving delay ⋮ Extremum principle for the Hadamard derivatives and its application to nonlinear fractional partial differential equations ⋮ An inverse time-dependent source problem for a time-space fractional diffusion equation ⋮ Cauchy problem for a fractional anisotropic parabolic equation in anisotropic Hölder spaces ⋮ Maximum principle and its application to multi-index Hadamard fractional diffusion equation

Cites Work

• Hopf's lemma and constrained radial symmetry for the fractional Laplacian
• Boundedness of weak solutions to evolutionary partial integro-differential equations with discontinuous coefficients
• Maximum principle for the generalized time-fractional diffusion equation
• Uniqueness and reconstruction of an unknown semilinear term in a time-fractional reaction–diffusion equation
• Maximum principle for the fractional diffusion equations with the Riemann-Liouville fractional derivative and its applications
• Regularity of the obstacle problem for a fractional power of the laplace operator
• Classical Fourier Analysis
• Unnamed Item

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