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Differential equations with random Gamma distributed moments of non-instantaneous impulses and p-moment exponential stability

Wybrane pełne teksty z tego czasopisma
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Nonlinear differential equations with impulses occurring at random time and acting noninstantaneously on finite intervals are studied. We consider the case when the time where the impulses occur is Gamma distributed. Lyapunov functions are applied to obtain sufficient conditions for the p-moment exponential stability of the trivial solution of the given system.
Wydawca
Rocznik
Strony
151--170
Opis fizyczny
Bibliogr. 23 poz., wykr.
Twórcy
autor
  • Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX 78363, USA Distinguished University Professor of Mathematics, Florida Institute of Technology, Melbourne, FL 32901, USA
autor
  • Department of Applied Mathematics and Modeling, University of Plovdiv, Plovdiv, Bulgaria
autor
  • School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland
autor
  • Department of Applied Mathematics and Modeling, University of Plovdiv, Plovdiv, Bulgaria
Bibliografia
  • [1] Hristova S., Integral stability in terms of two measures for impulsive functional differential equations, Math. Comput. Model., 2010, 51(1-2), 100-108
  • [2] Hristova S., Stability on a cone in terms of two measures for impulsive differential equations with “supremum”, Appl. Math. Lett., 2010, 23(5), 508-511
  • [3] Hristova S., Razumikhin method and cone valued Lyapunov functions for impulsive differential equations with “supremum“, Int. J. Dyn. Syst. Differ. Equ., 2009, 2, 223-236
  • [4] Hristova S., Stefanova K., Practical stability of impulsive differential equations with “supremum” by integral inequalities, Eur. J. Pure Appl. Math., 2012, 5, 30-44
  • [5] Hristova S., Lipschitz stability for impulsive differential equations with “supremum“, Int. Electron. J. Pure Appl. Math., 2010, 1, 345-358
  • [6] Hristova S., Georgieva A., Practical stability in terms of two measures for impulsive differential equations with “supremum”, Int. J. Differ. Equ., 2011, Article ID 703189
  • [7] Hristova S., Qualitative Investigations and Approximate Methods for Impulsive Differential Equations, Nova Science Publishers, New York, 2009
  • [8] Lakshmikantham V., Bainov D. D., Simeonov P. S., Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989
  • [9] Hernandez E., Pierri M., O’Regan D., On abstract differential equations with non instantaneous impulses, Topol. Methods Nonlinear Anal., 2015, 46(2), 1067-1088
  • [10] Agarwal R., O’Regan D., Hristova S., Stability by Lyapunov like functions of nonlinear differential equations with non-instantaneous impulses, J. Appl. Math. Comput., 2017, 53(1-2), 147-168
  • [11] Church K. E. M., Smith R. J., Existence and uniqueness of solutions of general impulsive extension equations with specification to linear equations, Dyn. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms, 2015, 22, 163-197
  • [12] Liao Y. M., Wang J. R., A note on stability of impulsive differential equations, Bound. Value Probl., 2014, 67
  • [13] Das S., Pandey D. N., Sukavanam N., Existence of solution of impulsive second order neutral integro-differential equations with state delay, J. Integral Equations Appl., 2015, 27(4), 489-520
  • [14] Agarwal R., O’Regan D., Hristova S., Stability of Caputo fractional differential equations with non-instantaneous impulses, Commun. Appl. Anal., (accepted)
  • [15] Kumar P., Pandey D. N., Bahuguna D., On a new class of abstract impulsive functional differential equations of fractional order, J. Nonlinear Sci. Appl., 2014, 7(2), 102-114
  • [16] Li P., Xu Ch., Boundary value problems of fractional order differential equation with integral boundary conditions and not instantaneous impulses, J. Funct. Spaces, 2015, Article ID 954925
  • [17] Sanz-Serna J. M., Stuart A. M., Ergodicity of dissipative differential equations subject to random impulses, J. Differential Equations, 1999, 155, 262-284
  • [18] Wu S., Hang D., Meng X., p-moment stability of stochastic equations with jumps, Appl. Math. Comput., 2004, 152, 505-519
  • [19] Wu H., Sun J., p-moment stability of stochastic differential equations with impulsive jump and Markovian switching, Automatica, 2006, 42(10), 1753-1759
  • [20] Yang J., Zhong S., Luo W., Mean square stability analysis of impulsive stochastic differential equations with delays, J. Comput. Appl. Math., 2008, 216(2), 474-483
  • [21] Anguraj A., Vinodkumar A., Existence, uniqueness and stability results of random impulsive semilinear differential systems, Nonlinear Anal. Hybrid Syst., 2010, 4(3), 475-483
  • [22] Wang J. R., Feckan M., Zhou Y., Random noninstantaneous impulsive models for studying periodic evolution processes in pharmacotherapy, In: Luo A., Merdan H. (Eds.) Mathematical Modeling and Applications in Nonlinear Dynamics, Nonlinear Systems and Complexity, 2016, 14, 87-107
  • [23] Kolmogorov A. N., Fomin S. V., Introductory Real Analysis, Dover Publ. Inc., New York, 1970
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-19e33c12-80eb-40ac-bacd-baa63f31ec45
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