Kochubei Anatoly Naumovich
Publications
Books:
A. N. Kochubei, Pseudo-Differential Equations and Stochastics over Non-Archimedean Fields, Marcel Dekker, New York, 2001.
S. D. Eidelman, S. D. Ivasyshen, and A. N. Kochubei, Analytic Methods in the Theory of Differential and Pseudo-Differential Equations of Parabolic Type, Birkhäuser, Basel, 2004.
A. N. Kochubei, Analysis in Positive Characteristic, Cambridge University Press, 2009.
Collective monograph (2 volumes):
“Handbook of Fractional Calculus with Applications (A.N. Kochubei and Yu. Luchko, Editors)”. Volume 1, “Basic Theory”– Berlin: De Gruyter, 2019, viii+481 pp. Volume 2, “Fractional Differential Equations” – Berlin: De Gruyter, 2019, viii+519 pp.
https://www.degruyter.com/view/title/534592?language=en
https://www.degruyter.com/view/title/534595
More than 130 research and survey papers in mathematics and physics. Almost all the papers published in 1997 and later are available from the ArXiv:
http://arxiv.org/find/grp_math/1/au:+kochubei/0/1/0/all/0/1
Publications for 2016-2024:
Chaotic property in general fractional calculus
Kochubei, Anatoly N.
Chaos 34 (2024), no. 12, Paper No. 123165, 6 pp.
https://doi.org/10.1063/5.0243475
Discrete-time general fractional calculus
Antoniouk, Alexandra V.; Kochubei, Anatoly N.
Fract. Calc. Appl. Anal. 27 (2024), no. 6, 2948–2963.
https://doi.org/10.1007/s13540-024-00350-9
Existence and uniqueness for p-adic counterpart of the porous medium equation
Antoniouk, Alexandra V.; Kochubei, Anatoly N.; Nikitchenko, Oleksii L.
J. Pseudo-Differ. Oper. Appl. 15 (2024), no. 4, Paper No. 79, 23 pp.
https://doi.org/10.1007/s11868-024-00647-6
The Vladimirov-Taibleson operator: inequalities, Dirichlet problem, boundary Hölder regularity. Kochubei, Anatoly N.
J. Pseudo-Differ. Oper. Appl. 14 (2023), no. 2, Paper No. 31, 27 pp.
https://doi.org/10.1007/s11868-023-00525-7
Pseudo-differential equations with weak degeneration for radial functions of p-adic argument
Antoniouk, Alexandra V.; Kochubei, Anatoly N.; Serdiuk, Mariia V.
J. Math. Anal. Appl. 523 (2023), no. 2, Paper No. 127026, 15 pp.
https://doi.org/10.1016/j.jmaa.2023.127026
Lp properties of non-Archimedean fractional differentiation operators
Kochubei, Anatoly N.
J. Pseudo-Differ. Oper. Appl. 12 (2021), no. 4, Paper No. 56, 14 pp.
https://doi.org/10.1007/s11868-021-00428-5
A. N. Kochubei, Nonlinear pseudo-differential equations for radial real functions on a non-Archimedean field. J. Math. Anal. Appl. 483 (2020), no. 1, 123609, 11 pp. Q1 (Scopus)
https://doi.org/10.1016/j.jmaa.2019.123609
A. N. Kochubei and Yu. G. Kondratiev, Growth Equation of the General Fractional Calculus, Mathematics 2019, 7, article 615; doi:10.3390/math7070615. Q1 (WoS)
https://doi.org/10.3390/math7070615
A. N. Kochubei and A. Khrennikov, p-Adic analogue of the porous medium equations, J. Fourier Anal. Appl. 24, No. 5 (2018), 1401-1424. Q1 (Scopus) https://doi.org/10.1007/s00041-017-9556-4
A. N. Kochubei and Yu. Kondratiev, Fractional kinetic hierarchies and intermittency, Kinetic and Related Models 10 (2017), 725 – 740. Q1 (Scopus) doi: 10.3934/krm.2017029
A. N. Kochubei, Non-Archimedean duality: algebras, groups, and multipliers, Algebras and Representation Theory, Vol. 19, No. 5 (2016), 1081-1108. Q1 (Scopus)
https://doi.org/10.1007/s10468-016-9612-9
A. Khrennikov and A. N. Kochubei, On the p-adic Navier-Stokes equation. Applicable. Anal. 99 (2020), no. 8, 1425–1435. Q2 (Scopus) https://doi.org/10.1080/00036811.2018.1533120
A. N. Kochubei, Yu. Kondratiev and J. L. da Silva, Random time change and related evolution equations. Time asymptotic behavior. Stochastics and Dynamics 20 (2020), no. 5, 2050034, 24 pp. Q2 (Scopus) https://doi.org/10.1142/S0219493720500343
A. V. Antoniouk, K. Oleschko, A. N. Kochubei and A. Yu. Khrennikov, A stochastic p-adic model of the capillary flow in porous random medium, Physica A, 505 (2018), 763-777. Q2 (Scopus)
https://doi.org/10.1016/j.physa.2018.03.049
A. N. Kochubei and Yu. G. Kondratiev, Fractional approximation of solutions of evolution equations, Analysis, Vol. 36, No. 2 (2016), 71-73. Q2 (Scopus)
https://doi.org/10.1515/anly-2015-5007
A. N. Kochubei and Yu. Kondratiev, Representations of the infinite-dimensional p-adic affine group. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 23 (2020), no. 1, 2050002, 11 pp. Q3 (Scopus) https://doi.org/10.1142/S0219025720500022
A. V. Antoniouk, A. Khrennikov and A. N. Kochubei, Multidimensional nonlinear pseudo-differential evolution equation with p-adic spatial variables. J. Pseudo-Differ. Oper. Appl. 11 (2020), no. 1, 311–343. Q3 (Scopus) https://doi.org/10.1007/s11868-019-00320-3
A. N. Kochubei, Linear and nonlinear heat equations on a p-adic ball, Ukrainian Math. J., 70, No. 2 (2018), 217-231. Q3 (Scopus) http://umj.imath.kiev.ua/index.php/umj/article/view/1550
J. L. Da Silva, A. N. Kochubei and Yu. G. Kondratiev, Fractional statistical dynamics and fractional kinetics, Meth. Funct. Anal. Topology, Vol. 22, No. 3 (2016), 197-209.
http://mfat.imath.kiev.ua/article/?id=890
A. N. Kochubei, D. S. Soskin, Asymptotic properties of the p-adic fractional integration operator. Methods Funct. Anal. Topology 23 (2017), no. 2, 155–163. http://mfat.imath.kiev.ua/article/?id=969
A. N. Kochubei, Pseudo-Differential Equations and Stochastics over Non-Archimedean Fields, Marcel Dekker, New York, 2001.
S. D. Eidelman, S. D. Ivasyshen, and A. N. Kochubei, Analytic Methods in the Theory of Differential and Pseudo-Differential Equations of Parabolic Type, Birkhäuser, Basel, 2004.
A. N. Kochubei, Analysis in Positive Characteristic, Cambridge University Press, 2009.
Collective monograph (2 volumes):
“Handbook of Fractional Calculus with Applications (A.N. Kochubei and Yu. Luchko, Editors)”. Volume 1, “Basic Theory”– Berlin: De Gruyter, 2019, viii+481 pp. Volume 2, “Fractional Differential Equations” – Berlin: De Gruyter, 2019, viii+519 pp.
https://www.degruyter.com/view/title/534592?language=en
https://www.degruyter.com/view/title/534595
More than 130 research and survey papers in mathematics and physics. Almost all the papers published in 1997 and later are available from the ArXiv:
http://arxiv.org/find/grp_math/1/au:+kochubei/0/1/0/all/0/1
Publications for 2016-2024:
Chaotic property in general fractional calculus
Kochubei, Anatoly N.
Chaos 34 (2024), no. 12, Paper No. 123165, 6 pp.
https://doi.org/10.1063/5.0243475
Discrete-time general fractional calculus
Antoniouk, Alexandra V.; Kochubei, Anatoly N.
Fract. Calc. Appl. Anal. 27 (2024), no. 6, 2948–2963.
https://doi.org/10.1007/s13540-024-00350-9
Existence and uniqueness for p-adic counterpart of the porous medium equation
Antoniouk, Alexandra V.; Kochubei, Anatoly N.; Nikitchenko, Oleksii L.
J. Pseudo-Differ. Oper. Appl. 15 (2024), no. 4, Paper No. 79, 23 pp.
https://doi.org/10.1007/s11868-024-00647-6
The Vladimirov-Taibleson operator: inequalities, Dirichlet problem, boundary Hölder regularity. Kochubei, Anatoly N.
J. Pseudo-Differ. Oper. Appl. 14 (2023), no. 2, Paper No. 31, 27 pp.
https://doi.org/10.1007/s11868-023-00525-7
Pseudo-differential equations with weak degeneration for radial functions of p-adic argument
Antoniouk, Alexandra V.; Kochubei, Anatoly N.; Serdiuk, Mariia V.
J. Math. Anal. Appl. 523 (2023), no. 2, Paper No. 127026, 15 pp.
https://doi.org/10.1016/j.jmaa.2023.127026
Lp properties of non-Archimedean fractional differentiation operators
Kochubei, Anatoly N.
J. Pseudo-Differ. Oper. Appl. 12 (2021), no. 4, Paper No. 56, 14 pp.
https://doi.org/10.1007/s11868-021-00428-5
A. N. Kochubei, Nonlinear pseudo-differential equations for radial real functions on a non-Archimedean field. J. Math. Anal. Appl. 483 (2020), no. 1, 123609, 11 pp. Q1 (Scopus)
https://doi.org/10.1016/j.jmaa.2019.123609
A. N. Kochubei and Yu. G. Kondratiev, Growth Equation of the General Fractional Calculus, Mathematics 2019, 7, article 615; doi:10.3390/math7070615. Q1 (WoS)
https://doi.org/10.3390/math7070615
A. N. Kochubei and A. Khrennikov, p-Adic analogue of the porous medium equations, J. Fourier Anal. Appl. 24, No. 5 (2018), 1401-1424. Q1 (Scopus) https://doi.org/10.1007/s00041-017-9556-4
A. N. Kochubei and Yu. Kondratiev, Fractional kinetic hierarchies and intermittency, Kinetic and Related Models 10 (2017), 725 – 740. Q1 (Scopus) doi: 10.3934/krm.2017029
A. N. Kochubei, Non-Archimedean duality: algebras, groups, and multipliers, Algebras and Representation Theory, Vol. 19, No. 5 (2016), 1081-1108. Q1 (Scopus)
https://doi.org/10.1007/s10468-016-9612-9
A. Khrennikov and A. N. Kochubei, On the p-adic Navier-Stokes equation. Applicable. Anal. 99 (2020), no. 8, 1425–1435. Q2 (Scopus) https://doi.org/10.1080/00036811.2018.1533120
A. N. Kochubei, Yu. Kondratiev and J. L. da Silva, Random time change and related evolution equations. Time asymptotic behavior. Stochastics and Dynamics 20 (2020), no. 5, 2050034, 24 pp. Q2 (Scopus) https://doi.org/10.1142/S0219493720500343
A. V. Antoniouk, K. Oleschko, A. N. Kochubei and A. Yu. Khrennikov, A stochastic p-adic model of the capillary flow in porous random medium, Physica A, 505 (2018), 763-777. Q2 (Scopus)
https://doi.org/10.1016/j.physa.2018.03.049
A. N. Kochubei and Yu. G. Kondratiev, Fractional approximation of solutions of evolution equations, Analysis, Vol. 36, No. 2 (2016), 71-73. Q2 (Scopus)
https://doi.org/10.1515/anly-2015-5007
A. N. Kochubei and Yu. Kondratiev, Representations of the infinite-dimensional p-adic affine group. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 23 (2020), no. 1, 2050002, 11 pp. Q3 (Scopus) https://doi.org/10.1142/S0219025720500022
A. V. Antoniouk, A. Khrennikov and A. N. Kochubei, Multidimensional nonlinear pseudo-differential evolution equation with p-adic spatial variables. J. Pseudo-Differ. Oper. Appl. 11 (2020), no. 1, 311–343. Q3 (Scopus) https://doi.org/10.1007/s11868-019-00320-3
A. N. Kochubei, Linear and nonlinear heat equations on a p-adic ball, Ukrainian Math. J., 70, No. 2 (2018), 217-231. Q3 (Scopus) http://umj.imath.kiev.ua/index.php/umj/article/view/1550
J. L. Da Silva, A. N. Kochubei and Yu. G. Kondratiev, Fractional statistical dynamics and fractional kinetics, Meth. Funct. Anal. Topology, Vol. 22, No. 3 (2016), 197-209.
http://mfat.imath.kiev.ua/article/?id=890
A. N. Kochubei, D. S. Soskin, Asymptotic properties of the p-adic fractional integration operator. Methods Funct. Anal. Topology 23 (2017), no. 2, 155–163. http://mfat.imath.kiev.ua/article/?id=969