Two equivalent Stefan's problems for the time fractional diffusion equation

DOI10.2478/s13540-013-0050-7zbMath1312.35191arXiv1306.1750OpenAlexW1986503280MaRDI QIDQ2347374

Eduardo Marcus, Sabrina D. Roscani

Publication date: 27 May 2015

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

Full work available at URL: https://arxiv.org/abs/1306.1750

zbMATH Keywords

Caputo's fractional derivativefractional diffusion equationStefan's problem

Mathematics Subject Classification ID

Stefan problems, phase changes, etc. (80A22) Mittag-Leffler functions and generalizations (33E12) Free boundary problems for PDEs (35R35) Moving boundary problems for PDEs (35R37) Fractional partial differential equations (35R11)

Related Items (14)

On the initial-boundary-value problem for the time-fractional diffusion equation on the real positive semiaxis ⋮ Numerical solution of the one phase 1D fractional Stefan problem using the front fixing method ⋮ Turán type inequalities for q-Mittag-Leffler and q-Wright functions ⋮ Determination of two unknown thermal coefficients through an inverse one-phase fractional Stefan problem ⋮ A note on models for anomalous phase-change processes ⋮ A new equivalence of Stefan’s problems for the time fractional diffusion equation ⋮ Hopf lemma for the fractional diffusion operator and its application to a fractional free-boundary problem ⋮ Fractional Stefan problem: a survey of the recent results ⋮ A new mathematical formulation for a phase change problem with a memory flux ⋮ Explicit solutions to fractional Stefan-like problems for Caputo and Riemann-Liouville derivatives ⋮ Mathematical analysis of a Cauchy problem for the time-fractional diffusion-wave equation with \( \alpha \in (0,2) \) ⋮ Explicit solution for a two-phase fractional Stefan problem with a heat flux condition at the fixed face ⋮ An integral relationship for a fractional one-phase Stefan problem ⋮ The similarity method and explicit solutions for the fractional space one-phase Stefan problems

Cites Work

• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• Some exact solutions to Stefan problems with fractional differential equations
• The fundamental solution of the space-time fractional diffusion equation
• An inequality for the coefficient 𝜎 of the free boundary 𝑠(𝑡)=2𝜎√𝑡 of the Neumann solution for the two-phase Stefan problem
• THE GENERALIZED BESSEL FUNCTION OF ORDER GREATER THAN ONE
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