The higher-order heat-type equations via signed Lévy stable and generalized Airy functions

DOI10.1088/1751-8113/46/42/425001zbMath1281.82021arXiv1305.3935OpenAlexW3099889536WikidataQ116677422 ScholiaQ116677422MaRDI QIDQ2857962

Andrzej Horzela, Katarzyna Górska, Karol A. Penson, Giuseppe Dattoli

Publication date: 19 November 2013

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.3935

zbMATH Keywords

integral transformsLévy processesrandom processesstatistical physicshigher-order heat-type equations

Mathematics Subject Classification ID

Brownian motion (60J65) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) PDEs in connection with statistical mechanics (35Q82)

Related Items (15)

Theory of relativistic heat polynomials and one-sided Lévy distributions ⋮ On fractional calculus of \(\mathcal A_{2n+1}(x)\) function ⋮ Mittag-Leffler function and fractional differential equations ⋮ The Atiyah-Singer index theorem for a family of fractional Dirac operators on spin geometry ⋮ Higher-order heat equation and the Gelfand-Dickey hierarchy ⋮ Green's functions and the Cauchy problem of the Burgers hierarchy and forced Burgers equation ⋮ On Mellin transforms of solutions of differential equation \(\chi^{(n)}(x)+\gamma_nx\chi (x)=0\) ⋮ Integral representations of products of airy functions related to fractional calculus ⋮ On the zeros of the Pearcey integral and a Rayleigh-type equation ⋮ The stretched exponential behavior and its underlying dynamics. The phenomenological approach ⋮ Photoluminescence decay of silicon nanocrystals and Lévy stable distributions ⋮ On the generalized mass transfer with a chemical reaction: Fractional derivative model ⋮ Operational, umbral methods, Borel transform and negative derivative operator techniques ⋮ Unnamed Item ⋮ Modular forms, Schwarzian conditions, and symmetries of differential equations in physics

This page was built for publication: The higher-order heat-type equations via signed Lévy stable and generalized Airy functions