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Stochastic Analysis and Applications Volume 32, 2014 - Issue 6
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Original Articles

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

Mirko D’ovidioDepartment of Basic and Applied Sciences for Engineers, Sapienza University of Rome, Rome, Italy
,
Enzo OrsingherDepartment of Statistical Sciences, Sapienza University of Rome, Rome, Italy
&
Bruno ToaldoDepartment of Statistical Sciences, Sapienza University of Rome, Rome, ItalyCorrespondence[email protected]
Pages 1009-1045 | Received 08 May 2014, Accepted 02 Sep 2014, Published online: 21 Oct 2014

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Ram K. Saxena, Roberto Garra & Enzo Orsingher. (2016) Analytical solution of space-time fractional telegraph-type equations involving Hilfer and Hadamard derivatives. Integral Transforms and Special Functions 27:1, pages 30-42.
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Luisa Beghin. (2015) Fractional Gamma and Gamma-Subordinated Processes. Stochastic Analysis and Applications 33:5, pages 903-926.
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Articles from other publishers (39)

Mirko D’Ovidio & Francesco Iafrate. (2024) Elastic drifted Brownian motions and non-local boundary conditions. Stochastic Processes and their Applications 167, pages 104228.
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Wensheng Wang. (2023) Temporal Fractal Nature of the Time-Fractional SPIDEs and Their Gradient. Fractal and Fractional 7:11, pages 815.
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Costantino Ricciuti & Bruno Toaldo. (2023) From Semi-Markov Random Evolutions to Scattering Transport and Superdiffusion. Communications in Mathematical Physics 401:3, pages 2999-3042.
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Thomas M. Michelitsch, Federico Polito & Alejandro P. Riascos. (2023) Semi-Markovian Discrete-Time Telegraph Process with Generalized Sibuya Waiting Times. Mathematics 11:2, pages 471.
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Mirko D’Ovidio. (2022) On the Non-Local Boundary Value Problem from the Probabilistic Viewpoint. Mathematics 10:21, pages 4122.
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Luisa Beghin, Roberto Garra, Francesco Mainardi & Gianni Pagnini. (2022) The tempered space-fractional Cattaneo equation. Probabilistic Engineering Mechanics 70, pages 103374.
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N. Vieira, M. Ferreira & M.M. Rodrigues. (2022) Time-fractional telegraph equation with ψ-Hilfer derivatives. Chaos, Solitons & Fractals 162, pages 112276.
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Wensheng Wang. (2021) Variations of the solution to a fourth order time-fractional stochastic partial integro-differential equation. Stochastics and Partial Differential Equations: Analysis and Computations 10:2, pages 582-613.
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Mirko D’Ovidio. (2022) Fractional boundary value problems. Fractional Calculus and Applied Analysis 25:1, pages 29-59.
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Nelson Vieira, M. Manuela Rodrigues & Milton Ferreira. (2022) Time-fractional telegraph equation of distributed order in higher dimensions with Hilfer fractional derivatives. Electronic Research Archive 30:10, pages 3595-3631.
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Jaume Masoliver. (2021) Telegraphic Transport Processes and Their Fractional Generalization: A Review and Some Extensions. Entropy 23:3, pages 364.
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Wensheng Wang. (2021) Spatial Moduli of Non-Differentiability for Time-Fractional SPIDEs and Their Gradient. Symmetry 13:3, pages 380.
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Luisa Beghin, Claudio Macci & Barbara Martinucci. (2020) Random time-changes and asymptotic results for a class of continuous-time Markov chains on integers with alternating rates. Modern Stochastics: Theory and Applications, pages 63-91.
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Francesco Iafrate & Enzo Orsingher. (2020) On the Fractional Wave Equation. Mathematics 8:6, pages 874.
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L Angelani & R Garra. (2020) On fractional Cattaneo equation with partially reflecting boundaries. Journal of Physics A: Mathematical and Theoretical 53:8, pages 085204.
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Raffaela Capitanelli & Mirko D’Ovidio. (2020) Delayed and rushed motions through time change. Latin American Journal of Probability and Mathematical Statistics 17:1, pages 183.
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Jaume Masoliver & Katja Lindenberg. (2020) Two-dimensional telegraphic processes and their fractional generalizations. Physical Review E 101:1.
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R. Garra, E. Orsingher & E. L. Shishkina. (2019) Solutions to Non-linear Euler-Poisson-Darboux Equations by Means of Generalized Separation of Variables. Lobachevskii Journal of Mathematics 40:5, pages 640-647.
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Luca Angelani & Roberto Garra. (2018) Probability distributions for the run-and-tumble models with variable speed and tumbling rate. Modern Stochastics: Theory and Applications, pages 3-12.
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Anup Biswas & József Lőrinczi. (2019) Maximum Principles for Time-Fractional Cauchy Problems with Spatially Non-Local Components. Fractional Calculus and Applied Analysis 21:5, pages 1335-1359.
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Mirko D’Ovidio & Paola Loreti. (2018) Solutions of fractional logistic equations by Euler’s numbers. Physica A: Statistical Mechanics and its Applications 506, pages 1081-1092.
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Mirko D’Ovidio, Paola Loreti, Alireza Momenzadeh & Sima Sarv Ahrab. (2018) Determination of Order in Linear Fractional Differential Equations. Fractional Calculus and Applied Analysis 21:4, pages 937-948.
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Alexander D. Kolesnik. (2018) Linear combinations of the telegraph random processes driven by partial differential equations. Stochastics and Dynamics 18:04, pages 1850020.
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Antonio Di Crescenzo, Barbara Martinucci & Shelemyahu Zacks. (2017) Telegraph Process with Elastic Boundary at the Origin. Methodology and Computing in Applied Probability 20:1, pages 333-352.
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Mirko D’Ovidio, Francesco Iafrate & Enzo Orsingher. (2018) Drifted Brownian motions governed by fractional tempered derivatives. Modern Stochastics: Theory and Applications, pages 445-456.
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M. D'Ovidio & F. Polito. (2018) Fractional Diffusion--Telegraph Equations and Their Associated Stochastic Solutions. Theory of Probability & Its Applications 62:4, pages 552-574.
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Costantino Ricciuti & Bruno Toaldo. (2017) Semi-Markov Models and Motion in Heterogeneous Media. Journal of Statistical Physics 169:2, pages 340-361.
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Shu-Nan Li & Bing-Yang Cao. (2017) Mathematical and information-geometrical entropy for phenomenological Fourier and non-Fourier heat conduction. Physical Review E 96:3.
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Jaume Masoliver. (2017) Three-dimensional telegrapher's equation and its fractional generalization. Physical Review E 96:2.
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Hassan Allouba & Yimin Xiao. (2017) L-Kuramoto–Sivashinsky SPDEs vs. time-fractional SPIDEs: Exact continuity and gradient moduli, 1/2-derivative criticality, and laws. Journal of Differential Equations 263:2, pages 1552-1610.
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Jaume Masoliver & Katja Lindenberg. (2017) Continuous time persistent random walk: a review and some generalizations. The European Physical Journal B 90:6.
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Pietro Artale Harris & Roberto Garra. (2017) Nonlinear heat conduction equations with memory: Physical meaning and analytical results. Journal of Mathematical Physics 58:6.
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Ryszard Kutner & Jaume Masoliver. (2017) The continuous time random walk, still trendy: fifty-year history, state of art and outlook. The European Physical Journal B 90:3.
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Enzo Orsingher & Bruno Toaldo. (2015) Space–Time Fractional Equations and the Related Stable Processes at Random Time. Journal of Theoretical Probability 30:1, pages 1-26.
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Mirko D'Ovidio, Mirko D'Ovidio, Federico Polito & Federico Polito. (2017) Fractional diffusion-telegraph equations and their associated stochastic solutionsFractional diffusion-telegraph equations and their associated stochastic solutions. Теория вероятностей и ее применения Teoriya Veroyatnostei i ee Primeneniya 62:4, pages 692-718.
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Roberto Garra & Enzo Orsingher. 2017. Modern Problems of Stochastic Analysis and Statistics. Modern Problems of Stochastic Analysis and Statistics 25 39 .
Enzo Orsingher, Costantino Ricciuti & Bruno Toaldo. (2016) Time-Inhomogeneous Jump Processes and Variable Order Operators. Potential Analysis 45:3, pages 435-461.
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Roberto Garra. (2016) On the generalized Hardy–Hardy–Maurer model with memory effects. Nonlinear Dynamics 86:2, pages 861-868.
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Jaume Masoliver. (2016) Fractional telegrapher's equation from fractional persistent random walks. Physical Review E 93:5.
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