The fundamental solutions for the fractional diffusion-wave equation
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Publication:1352355
DOI10.1016/0893-9659(96)00089-4zbMath0879.35036OpenAlexW2081531908WikidataQ127443312 ScholiaQ127443312MaRDI QIDQ1352355
Publication date: 22 December 1997
Published in: Applied Mathematics Letters (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0893-9659(96)00089-4
Laplace transformwave equationfractional derivativesGreen's functiondiffusion equationWright functionsignalling problems
Fundamental solutions to PDEs (35A08) Fractional derivatives and integrals (26A33) Initial value problems for linear higher-order PDEs (35G10)
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Cites Work
