A uniqueness determination of the fractional exponents in a three-parameter fractional diffusion

DOI10.7153/fdc-2023-13-04arXiv1810.01543OpenAlexW3025595395MaRDI QIDQ6196494

Süleyman Ulusoy, Hans Werner van Wyk, Erkan Nane, Ngartelbaye Guerngar

Publication date: 14 March 2024

Published in: Fractional Differential Calculus (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.01543

zbMATH Keywords

Mittag-Leffler functionweak solutioninverse problem\(\alpha\)-stable processCaputo derivativefractional Laplacian

Mathematics Subject Classification ID

Ill-posed problems for PDEs (35R25) Inverse problems for PDEs (35R30) Series solutions to PDEs (35C10) Fractional partial differential equations (35R11)

Cites Work

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• Inverse source problem with a final overdetermination for a fractional diffusion equation
• Space-time fractional diffusion on bounded domains
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• Dirichlet forms and symmetric Markov processes
• Perturbation by non-local operators
• A novel and accurate finite difference method for the fractional Laplacian and the fractional Poisson problem
• Analytic methods in the theory of differential and pseudo-differential equations of parabolic type
• Dirichlet heat kernel estimates for \(\Delta ^{\alpha /2} + \delta ^{\beta /2}\)
• Simultaneous inversion for the fractional exponents in the space-time fractional diffusion equation \(\partial_t^\beta u = -(-\Delta)^{\alpha /2}u -(-\Delta)^{\gamma /2}u\)
• Factorization and estimates of Dirichlet heat kernels for non-local operators with critical killings
• Two-sided eigenvalue estimates for subordinate processes in domains
• Simultaneous inversion for the exponents of the fractional time and space derivatives in the space-time fractional diffusion equation
• Simultaneous inversion for the space-dependent diffusion coefficient and the fractional order in the time-fractional diffusion equation
• Stochastic solution of space-time fractional diffusion equations
• An inverse problem for a one-dimensional time-fractional diffusion problem
• Carleman estimate for a fractional diffusion equation with half order and application
• Conditional stability in determining a zeroth-order coefficient in a half-order fractional diffusion equation by a Carleman estimate
• Uniqueness in an inverse problem for a one-dimensional fractional diffusion equation
• The fundamental solution of the space-time fractional diffusion equation
• A backward problem for the time-fractional diffusion equation

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