Mathematical analysis of a Cauchy problem for the time-fractional diffusion-wave equation with \( \alpha \in (0,2) \)

DOI10.1007/s00041-017-9527-9zbMath1394.35553OpenAlexW2605856890MaRDI QIDQ1746606

Demian Nahuel Goos, Gabriela Fernanda Reyero

Publication date: 25 April 2018

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

Full work available at URL: https://doi.org/10.1007/s00041-017-9527-9

zbMATH Keywords

Fourier transformMittag-Leffler functionCauchy problemCaputo fractional derivativeMainardi functiontime-fractional diffusion-wave equation

Mathematics Subject Classification ID

Mittag-Leffler functions and generalizations (33E12) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Initial value problems for linear higher-order PDEs (35G10) Fractional partial differential equations (35R11)

Cites Work

• On the initial-boundary-value problem for the time-fractional diffusion equation on the real positive semiaxis
• Front propagation in anomalous diffusive media governed by time-fractional diffusion
• Dirichlet problem for the generalized Laplace equation with the Caputo derivative
• Existence and uniqueness of the solution for a time-fractional diffusion equation with Robin boundary condition
• Mittag-Leffler functions and their applications
• The \(M\)-Wright function in time-fractional diffusion processes: a tutorial survey
• Necessary and sufficient conditions for the fractional calculus of variations with Caputo derivatives
• Fractional diffusion equations by the Kansa method
• Fractional models, non-locality, and complex systems
• Implicit finite difference approximation for time fractional diffusion equations
• The Wright functions as solutions of the time-fractional diffusion equation.
• Cauchy problem for fractional diffusion equations
• Finite difference approximations for fractional advection-dispersion flow equations
• Two equivalent Stefan's problems for the time fractional diffusion equation
• Boundary value problems for fractional differential equations involving Caputo derivative in Banach spaces
• Some exact solutions to Stefan problems with fractional differential equations
• Approximation methods and stability of singular integral equations for Freud exponential weights on the line
• Maximum principle and its application for the time-fractional diffusion equations
• Maximum principle for the fractional diffusion equations with the Riemann-Liouville fractional derivative and its applications
• Fractional diffusion and wave equations
• Isoperimetric Problems of the Calculus of Variations on Time Scales
• Multi-dimensional fractional wave equation and some properties of its fundamental solution
• The fundamental solution of the space-time fractional diffusion equation
• Multi–dimensional solutions of space–time–fractional diffusion equations
• Initial-boundary-value problems for the one-dimensional time-fractional diffusion equation
• Fractional variational calculus and the transversality conditions
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item