Asymptotic estimates of solutions to initial-boundary-value problems for distributed order time-fractional diffusion equations

DOI10.2478/s13540-014-0217-xzbMath1312.35184OpenAlexW1985839840MaRDI QIDQ2347228

Yuri Luchko, Masahiro Yamamoto, Zhi-yuan Li

Publication date: 27 May 2015

Published in: Fractional Calculus \& Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2478/s13540-014-0217-x

zbMATH Keywords

Laplace transformlong-time asymptotic behaviorinitial-boundary-value problemsdistributed order fractional diffusion equationshort-time asymptotic behavior

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Laplace transform (44A10) Fractional partial differential equations (35R11)

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Cites Work

• Modeling anomalous heat transport in geothermal reservoirs via fractional diffusion equations
• Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems
• Initial-boundary-value problems for the generalized multi-term time-fractional diffusion equation
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• Fundamental solution of a distributed order time-fractional diffusion-wave equation as probability density
• Distributed order calculus and equations of ultraslow diffusion
• Stochastic model for ultraslow diffusion
• Regularity and Unique Existence of Solution to Linear Diffusion Equation with Multiple Time-Fractional Derivatives
• Time-fractional Diffusion of Distributed Order
• Distributed order derivatives and relaxation patterns
• DISTRIBUTED ORDER FRACTIONAL SUB-DIFFUSION
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