Zobrazeno 1 - 10
of 218
pro vyhledávání: '"Mark M. Meerschaert"'
Publikováno v:
International Journal of Differential Equations, Vol 2010 (2010)
Externí odkaz:
https://doaj.org/article/c7d64f8d99de40d7add796f0bf3dd6f5
Autor:
Mark M. Meerschaert, Alla Sikorskii
Fractional calculus is a rapidly growing field of research, at the interface between probability, differential equations, and mathematical physics. It is used to model anomalous diffusion, in which a cloud of particles spreads in a different manner t
Publikováno v:
Journal of Time Series Analysis. 42:442-470
Climate data often provides a periodically stationary time series, due to seasonal variations in the mean and covariance structure. Periodic ARMA models, where the parameters vary with the season, capture the nonstationary behavior. High frequency da
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::9ee64bc9b33028e3e070de3e42120e45
https://doi.org/10.1111/jtsa.12579
https://doi.org/10.1111/jtsa.12579
Publikováno v:
Communications on Applied Mathematics and Computation. 3:61-90
Fractional calculus and fractional-order modeling provide effective tools for modeling and simulation of anomalous diffusion with power-law scalings. In complex multi-fractal anomalous transport phenomena, distributed-order partial differential equat
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::3a522adf509c504bb8a7267286da50ff
https://doi.org/10.1007/s42967-020-00070-w
https://doi.org/10.1007/s42967-020-00070-w
Publikováno v:
Fractional Calculus and Applied Analysis. 22:1561-1595
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::bae042cc211ec67f200d757841239acb
https://doi.org/10.1515/fca-2019-0081
https://doi.org/10.1515/fca-2019-0081
Autor:
Bruno Toaldo, Mark M. Meerschaert
Publikováno v:
Stochastic Processes and their Applications. 129:2850-2879
Exponential relaxation to equilibrium is a typical property of physical systems, but inhomogeneities are known to distort the exponential relaxation curve, leading to a wide variety of relaxation patterns. Power law relaxation is related to fractiona
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bea5ce950500489d956c4becdf42066d
https://doi.org/10.1016/j.spa.2018.08.004
https://doi.org/10.1016/j.spa.2018.08.004
Publikováno v:
Fractional Calculus and Applied Analysis. 22:326-357
It is well known that certain fractional diffusion equations can be solved by the densities of stable L\'evy motions. In this paper we use the classical semigroup approach for L\'evy processes to define semi-fractional derivatives, which allows us to
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d336418a2e486abddaa9047e9c2c1d93
https://doi.org/10.1515/fca-2019-0021
https://doi.org/10.1515/fca-2019-0021
Publikováno v:
Journal of Computational Physics. 376:1089-1107
This paper develops appropriate boundary conditions for the two-sided fractional diffusion equation, where the usual second derivative in space is replaced by a weighted average of positive (left) and negative (right) fractional derivatives. Mass pre
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::3e524a42d69c59928113747250d4f53b
https://doi.org/10.1016/j.jcp.2018.10.010
https://doi.org/10.1016/j.jcp.2018.10.010
Publikováno v:
Journal of Computational and Applied Mathematics. 339:161-178
Anomalous diffusion with ballistic scaling is characterized by a linear spreading rate with respect to time that scales like pure advection. Ballistic scaling may be modeled with a symmetric Riesz derivative if the spreading is symmetric. However, ba
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::15b487942a1d102a5f034fe30e847bf6
https://doi.org/10.1016/j.cam.2017.11.012
https://doi.org/10.1016/j.cam.2017.11.012
Publikováno v:
Journal of Computational and Applied Mathematics. 339:414-430
This paper derives physically meaningful boundary conditions for fractional diffusion equations, using a mass balance approach. Numerical solutions are presented, and theoretical properties are reviewed, including well-posedness and steady state solu
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::63e6ba174baadbeba787cf8ee06e5a39
https://doi.org/10.1016/j.cam.2018.03.007
https://doi.org/10.1016/j.cam.2018.03.007