A new regularization method for solving a time-fractional inverse diffusion problem

DOI10.1016/j.jmaa.2011.01.067zbMath1211.35281OpenAlexW2008160098MaRDI QIDQ633643

Juan-Miguel Gracia

Publication date: 29 March 2011

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2011.01.067

zbMATH Keywords

Fourier transformLaplace transformtemperatureregularization methodheat fluxCaputo's fractional derivatives

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Inverse problems for PDEs (35R30) Transform methods (e.g., integral transforms) applied to PDEs (35A22) Numerical methods for discrete and fast Fourier transforms (65T50) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32) Inverse problems in thermodynamics and heat transfer (80A23) Fractional partial differential equations (35R11)

Related Items (22)

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Cites Work

• Unnamed Item
• A modified tanh-coth method for solving the general Burgers-Fisher and the Kuramoto-Sivashinsky equations
• Well-posedness for the fifth-order shallow water equations
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• The fundamental solutions for the fractional diffusion-wave equation
• Fractional diffusion equation for fractal-time-continuous-time random walks
• Time fractional IHCP with Caputo fractional derivatives
• Stable numerical solution of a fractional-diffusion inverse heat conduction problem
• Determining Surface Temperatures from Interior Observations
• Fractional diffusion equation on fractals: one-dimensional case and asymptotic behaviour
• Fractional diffusion equation on fractals: three-dimensional case and scattering function
• The fundamental solution of the space-time fractional diffusion equation
• Wavelet and Fourier Methods for Solving the Sideways Heat Equation
• Continuous-time random walks and the fractional diffusion equation
• A general solution of the diffusion equation for semiinfinite geometries
• The random walk's guide to anomalous diffusion: A fractional dynamics approach

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