Applications of integral transforms in fractional diffusion processes

DOI10.1080/10652460412331270652zbMath1093.45003arXiv0710.0145OpenAlexW2962721443MaRDI QIDQ4659490

Francesco Mainardi

Publication date: 21 March 2005

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

Full work available at URL: https://arxiv.org/abs/0710.0145

zbMATH Keywords

Fourier transformLaplace transformsMellin transformsfractional differential equationsCaputo fractional derivativeGreen's function solutionfractional diffusion processesRiesz-Feller fractional

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) Fractional derivatives and integrals (26A33) Heat equation (35K05) Transform methods (e.g., integral transforms) applied to PDEs (35A22) Diffusion processes (60J60) Mittag-Leffler functions and generalizations (33E12) Laplace transform (44A10) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38)

Related Items (7)

THE METHOD OF GREEN‘S FUNCTION FOR ONE DIFFERENTIAL EQUATION OF A FRACTIONAL ORDER ⋮ Boundary value problems for a moisture transfer equation with the Caputo fractional derivative and the Bessel operator ⋮ A scaling method and its applications to problems in fractional dimensional space ⋮ Boundary value problems for a pseudoparabolic equation with the Caputo fractional derivative ⋮ A class of self-similar stochastic processes with stationary increments to model anomalous diffusion in physics ⋮ Discrete-space time-fractional processes ⋮ Existence and regularity results for stochastic fractional pseudo-parabolic equations driven by white noise

Cites Work

• Fractional relaxation-oscillation and fractional diffusion-wave phenomena.
• Fractals and fractional calculus in continuum mechanics
• Wright functions as scale-invariant solutions of the diffusion-wave equation
• On Mittag-Leffler-type functions in fractional evolution processes
• Salvatore Pincherle: the pioneer of the Mellin-Barnes integrals.
• L'intégrale de Riemann-Liouville et le problème de Cauchy
• Chance and Stability
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