Time-Changed Processes Governed by Space-Time Fractional Telegraph Equations

DOI10.1080/07362994.2014.962046zbMath1309.60046arXiv1206.2511OpenAlexW2124708659MaRDI QIDQ2937464

Mirko D'Ovidio, Bruno Toaldo, Enzo Orsingher

Publication date: 9 January 2015

Published in: Stochastic Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1206.2511

zbMATH Keywords

Mittag-Leffler functionstelegraph processfractional LaplaciansubordinatorsRiemann-Liouville fractional calculusAiry functionstime-changed processestelegraph-type space-time fractional equation

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Fractional derivatives and integrals (26A33) Stable stochastic processes (60G52) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Solutions to PDEs in closed form (35C05) Fractional ordinary differential equations (34A08) Fractional partial differential equations (35R11) Functional-differential equations with fractional derivatives (34K37)

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Cites Work

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• Fractional powers of closed operators and the semigroups generated by them
• Reaction-diffusion systems and nonlinear waves
• Fractional diffusion equations and processes with randomly varying time
• Properties of the telegrapher's random process with or without a trap
• Time-fractional telegraph equations and telegraph processes with Brownian time
• The space-fractional telegraph equation and the related fractional telegraph process
• Brownian-time processes: The PDE connection and the half-derivative generator
• Iterated Brownian motion in an open set.
• Fractional telegraph-type equations and hyperbolic Brownian motion
• Random flights in higher spaces
• Analytic and approximate solutions of the space- and time-fractional telegraph equations
• Telegraph processes with random velocities
• INTERACTING TIME-FRACTIONAL AND Δ^ν PDES SYSTEMS VIA BROWNIAN-TIME AND INVERSE-STABLE-LÉVY-TIME BROWNIAN SHEETS
• Fractional kinetic equations: solutions and applications
• Diffusion Equation and Stochastic Processes

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