Analytical solution of the generalized space-time fractional ultra-hyperbolic differential equation

DOI10.1080/10652469.2021.1928661zbMath1495.35188OpenAlexW3163144254WikidataQ115295840 ScholiaQ115295840MaRDI QIDQ5063381

Gustavo Abel Dorrego

Publication date: 21 March 2022

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10652469.2021.1928661

zbMATH Keywords

fractional powerultra-hyperbolic operatorHilfer fractional derivativeFox's H-functionintegrals transformsMittag-Leffler-type function

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Transform methods (e.g., integral transforms) applied to PDEs (35A22) Mittag-Leffler functions and generalizations (33E12) Other functions defined by series and integrals (33E20) Solutions to PDEs in closed form (35C05) Fractional partial differential equations (35R11)

Cites Work

• Fundamental solutions of the time fractional diffusion-wave and parabolic Dirac operators
• Fractional relaxation-oscillation and fractional diffusion-wave phenomena.
• New function of Mittag-Leffler type and its application in the fractional diffusion-wave equation
• The fundamental solutions for the fractional diffusion-wave equation
• Some properties of the generalized causal and anticausal Riesz potentials.
• Mellin integral transform approach to analyze the multidimensional diffusion-wave equations
• Time-fractional diffusion equation in the fractional Sobolev spaces
• The Cauchy problem for the diffusion-wave equation with the Caputo partial derivative
• The Mittag–Leffler function and its application to the ultra-hyperbolic time-fractional diffusion-wave equation
• Solutions of the Fractional Reaction Equation and the Fractional Diffusion Equation
• Multidimensional solutions of space–fractional diffusion equations
• Multi–dimensional solutions of space–time–fractional diffusion equations
• Multidimensional solutions of time-fractional diffusion-wave equations
• Mittag-Leffler Functions, Related Topics and Applications
• Cauchy problems of fractional order and stable processes
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