Generalized Cattaneo–Maxwell diffusion equation with fractional derivatives. Dispersion relations

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dc.citation.epage68
dc.citation.issue1
dc.citation.spage58
dc.contributor.affiliationНаціональний університет “Львівська політехніка”
dc.contributor.affiliationІнститут фізики конденсованих систем НАН України
dc.contributor.affiliationLviv Polytechnic National University
dc.contributor.affiliationInstitute for Condensed Matter Physics of the National Academy of Sciences of Ukraine
dc.contributor.authorКостробій, П.
dc.contributor.authorМаркович, Б.
dc.contributor.authorВізнович, О.
dc.contributor.authorЗелінська, І.
dc.contributor.authorТокарчук, М.
dc.contributor.authorKostrobij, P.
dc.contributor.authorMarkovych, B.
dc.contributor.authorViznovych, O.
dc.contributor.authorZelinska, I.
dc.contributor.authorTokarchuk, M.
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2020-02-27T09:45:23Z
dc.date.available2020-02-27T09:45:23Z
dc.date.created2019-02-26
dc.date.issued2019-02-26
dc.description.abstractОтримано нове немарковське рівняння дифузії частинок у просторово неоднорідному середовищі з фрактальною структурою та узагальнене рівняння дифузії Кеттано–Максвелла з урахуванням просторово-часової нелокальності. Знайдено дисперсійні співвідношення для рівняння дифузії типу Кеттано–Максвелла з урахуванням просторово-часової нелокальності у дробових похідних. Розраховано частотний спектр, фазову та групову швидкості й показано його хвильову поведінку зі стрибкоподібними розривами, які проявляються також у зміні фазової швидкості.
dc.description.abstractThe new non-Markovian diffusion equations of ions in spatially heterogeneous environment with fractal structure and generalized Cattaneo–Maxwell diffusion equation with taking into account the space-time nonlocality are obtained. Dispersion relations for the Cattaneo–Maxwell-type diffusion equation with taking into account the space-time nonlocality in fractional derivatives are found. The frequency spectrum, phase and group velocities are calculated. It is shown that it has a wave behavior with discontinuities, which are also manifested in behavior of the phase velocity.
dc.format.extent58-68
dc.format.pages11
dc.identifier.citationGeneralized Cattaneo–Maxwell diffusion equation with fractional derivatives. Dispersion relations / P. Kostrobij, B. Markovych, O. Viznovych, I. Zelinska, M. Tokarchuk // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2019. — Vol 6. — No 1. — P. 58–68.
dc.identifier.citationenGeneralized Cattaneo–Maxwell diffusion equation with fractional derivatives. Dispersion relations / P. Kostrobij, B. Markovych, O. Viznovych, I. Zelinska, M. Tokarchuk // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2019. — Vol 6. — No 1. — P. 58–68.
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/46157
dc.language.isoen
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofMathematical Modeling and Computing, 1 (6), 2019
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dc.relation.referencesen42. SaichevA. I., ZaslavskyG.M. Fractional kinetic equations: solutions and applications. Chaos. 7 (4), 753–764 (1997).
dc.relation.referencesen43. ZaslavskyG.M., EdelmanM.A. Fractional kinetics: from pseudochaotic dynamics to Maxwell’s Demon. Physica D: Nonlinear Phenomena. 193 (1–4), 128–147 (2004).
dc.relation.referencesen44. NigmatullinR. ‘Fractional’ kinetic equations and ‘universal’ decoupling of a memory function in mesoscale region. Physica A: Statistical Mechanics and its Applications. 363 (2), 282–298 (2006).
dc.relation.referencesen45. ChechkinA.V., GoncharV.Y., Szyd lowskiM. Fractional kinetics for relaxation and superdiffusion in a magnetic field. Physics of Plasmas. 9 (1), 78–88 (2002).
dc.relation.referencesen46. GafiychukV.V., DatskoB.Y. Stability analysis and oscillatory structures in time-fractional reactiondiffusion systems. Phys. Rev. E. 75 (5), 055201 (2007).
dc.relation.referencesen47. Koszto lowiczT., LewandowskaK.D. Time evolution of the reaction front in a subdiffusive system. Phys. Rev. E. 78 (6), 066103 (2008).
dc.relation.referencesen48. ShkilevV.P. Subdiffusion of mixed origin with chemical reactions. Journal of Experimental and Theoretical Physics. 117 (6), 1066–1070 (2013).
dc.relation.referencesen49. HobbieR.K., RothB. J. Intermediate Physics for Medicine and Biology. Springer-Verlag, New York (2007).
dc.relation.referencesen50. Jeon J.H., MonneH.M. S., JavanainenM., MetzlerR. Anomalous Diffusion of Phospholipids and Cholesterols in a Lipid Bilayer and its Origins. Phys. Rev. Lett. 109 (18), 188103 (2012).
dc.relation.referencesen51. H¨ofling F., FranoschT. Anomalous transport in the crowded world of biological cells. Reports on Progress in Physics. 76 (4), 046602 (2013).
dc.relation.referencesen52. UchaikinV.V. Fractional phenomenology of cosmic ray anomalous diffusion. Physics-Uspekhi. 56 (11), 1074–1119 (2013).
dc.relation.referencesen53. Szymanski J., WeissM. Elucidating the Origin of Anomalous Diffusion in Crowded Fluids. Phys. Rev. Lett. 103 (3), 038102 (2009).
dc.relation.referencesen54. SandevT., Tomovski Z., DubbeldamJ. L.A., ChechkinA. Generalized diffusion-wave equation with memory kernel. Journal of Physics A: Mathematical and Theoretical. 52 (1), 015201 (2018).
dc.relation.referencesen55. SandevT., MetzlerR., ChechkinA. Generalised Diffusion and Wave Equations: Recent Advances. arXiv:1903.01166 (2019).
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dc.rights.holderCMM IAPMM NAS
dc.rights.holder© 2019 Lviv Polytechnic National University
dc.subjectузагальнене рівняння дифузії
dc.subjectнерівноважний статистичний оператор
dc.subjectстатистика Рені
dc.subjectчасова мультифрактальність
dc.subjectпросторова фрактальність
dc.subjectпросторово-часова фрактальність
dc.subjectgeneralized diffusion equation
dc.subjectnonequilibrium statistical operator
dc.subjectRenyi statistics
dc.subjectmultifractal time
dc.subjectspatial fractality
dc.subjectnonlocality of space-time
dc.subject.udc538.93
dc.titleGeneralized Cattaneo–Maxwell diffusion equation with fractional derivatives. Dispersion relations
dc.title.alternativeУзагальнене рівняння дифузії Кеттано–Максвелла у дробових похідних. Дисперсійні співвідношення
dc.typeArticle

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Mathematical Modeling And Computing. – 2019. – Vol. 6, No. 1