Zobrazeno 1 - 10
of 21
pro vyhledávání: '"Luděk Nechvátal"'
Publikováno v:
Abstract and Applied Analysis, Vol 2011 (2011)
This paper investigates some initial value problems in discrete fractional calculus. We introduce a linear difference equation of fractional order along with suitable initial conditions of fractional type and prove the existence and uniqueness of the
Externí odkaz:
https://doaj.org/article/d5367d39b51b4207b91f945d1311b274
Autor:
Luděk Nechvátal, Jan Cermak
Publikováno v:
Nonlinear Dynamics. 104:1253-1267
This paper discusses the problem of linearized stability for nonlinear fractional difference equations. Computational methods based on appropriate linearization theorem are standardly applied in bifurcation analysis of dynamical systems. However, in
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::8ca62f184dda97ea2a179fb4d6fd0ee6
https://doi.org/10.1007/s11071-021-06372-9
https://doi.org/10.1007/s11071-021-06372-9
Autor:
Jan Cermak, Luděk Nechvátal
Publikováno v:
Chaos, Solitons & Fractals. 125:24-33
The paper provides a theoretical analysis of some local bifurcations in the fractional Chen system. Contrary to the integer-order case, basic bifurcation properties of the fractional Chen system are shown to be qualitatively different from those desc
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::dc74921e898e5fd99f65bfb22b3ecf42
https://doi.org/10.1016/j.chaos.2019.05.007
https://doi.org/10.1016/j.chaos.2019.05.007
Autor:
Jan Cermak, Luděk Nechvátal
Publikováno v:
Applied Mathematics Letters. 125:107750
The paper studies a class of linear differential equations with several delayed arguments formed by iterates of a given function. The main result of this paper improves the existing stability criteria and formulates an effective necessary and suffici
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::07fb893a101180b2d02c4320b40e7cec
https://doi.org/10.1016/j.aml.2021.107750
https://doi.org/10.1016/j.aml.2021.107750
Autor:
Jan Cermak, Luděk Nechvátal
Publikováno v:
Journal of Nonlinear Mathematical Physics. 17:51
The paper discusses fractional integrals and derivatives appearing in the so-called (q, h)-calculus which is reduced for h = 0 to quantum calculus and for q = h = 1 to difference calculus. We introduce delta as well as nabla version of these notions
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::02551688fbab426835219d832037140d
https://doi.org/10.1142/s1402925110000593
https://doi.org/10.1142/s1402925110000593
The Routh–Hurwitz conditions of fractional type in stability analysis of the Lorenz dynamical system
Autor:
Luděk Nechvátal, Jan Cermak
Publikováno v:
Nonlinear Dynamics. 87:939-954
This paper discusses stability conditions and a chaotic behavior of the Lorenz dynamical system involving the Caputo fractional derivative of orders between 0 and 1. Contrary to some existing results on the topic, we study these problems with respect
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::61a9117ebb6239a8290d097d6c112ae3
https://doi.org/10.1007/s11071-016-3090-9
https://doi.org/10.1007/s11071-016-3090-9
Autor:
Luděk Nechvátal, Jan Cermak
Publikováno v:
Applied Mathematics Letters. 105:106296
The paper discusses the problem of necessary and sufficient stability conditions for a test fractional delay differential equation and its discretization. First, we recall the existing condition for asymptotic stability of the exact equation and cons
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::df13ecf95ed510faa906e21f1b802a9b
https://doi.org/10.1016/j.aml.2020.106296
https://doi.org/10.1016/j.aml.2020.106296
Autor:
Luděk Nechvátal, Jan Cermak
Publikováno v:
Physica D: Nonlinear Phenomena. 404:132339
The paper discusses stabilizing effects of some time-delayed feedback controls applied to unstable steady states of an autonomous system of ordinary differential equations. First, we derive explicit delay-dependent stability conditions that are appli
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::708d0f0e37b56fa111ba8dd9a29f9a44
https://doi.org/10.1016/j.physd.2020.132339
https://doi.org/10.1016/j.physd.2020.132339
Autor:
Luděk Nechvátal
Publikováno v:
Scopus-Elsevier
The (modified) two-parametric Mittag-Leffler function plays an essential role in solving the so-called fractional differential equations. Its asymptotics is known (at least for a subset of its domain and special choices of the parameters). The aim of
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::dad4f1575acbe3dfc8bb265c62105df2
https://doi.org/10.21136/mb.2014.144143
https://doi.org/10.21136/mb.2014.144143
Autor:
Luděk Nechvátal
Publikováno v:
Tatra Mountains Mathematical Publications. 48:145-152
The paper deals with a nonlinear weak monotone type problem and its solution with respect to uncertain coefficients in the equation. The so- -called worst scenario method is adopted. The formulation of suitable conditions and a proof of the existence
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::be2967ef936de7fb6a4f09813eaf8fec
https://doi.org/10.2478/v10127-011-0014-4
https://doi.org/10.2478/v10127-011-0014-4