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Nonlinear fractional differential equations with non-instantaneous impulses in Banach spaces

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper is devoted to study the existence of solutions for a class of initial value problems for non-instantaneous impulsive fractional differential equations involving the Caputo fractional derivative in a Banach space. The arguments are based upon Monch's fixed point theorem and the technique of measures of noncompactness.
Rocznik
Tom
Strony
39--51
Opis fizyczny
Bibliogr. 25 poz.
Twórcy
autor
  • Laboratory of Mathematics, Djillali Liabes University of Sidi-Bel-Abbes, P.O. Box 89, Sidi Bel-Abbès 22000, Algeria
autor
  • Laboratory of Mathematics, Djillali Liabes University of Sidi-Bel-Abbes, P.O. Box 89, Sidi Bel-Abbès 22000, Algeria
Bibliografia
  • [1] S. Abbas, M. Benchohra, Uniqueness and Ulam stabilities results for partial fractional differential equations with not instantaneous impulses, Appl. Math. Comput. 257 (2015) 190-198.
  • [2] S. Abbas, M. Benchohra, M.A. Darwish, New stability results for partial fractional differential inclusions with not instantaneous impulses, Frac. Calc. Appl. Anal. 18 (1) (2015) 172-191.
  • [3] S. Abbas, M. Benchohra, G.M. N'Guérékata, Topics in Fractional Differential Equations, Springer-Verlag, New York, 2012.
  • [4] S. Abbas, M. Benchohra, G.M. N'Guérékata, Advanced Fractional Differential and Integral Equations, Nova Science Publishers, New York, 2015.
  • [5] R.P. Agarwal, S. Hristova, D. O'Regan, Non-Instantaneous Impulses in Differential Equations, Springer, New York, 2017.
  • [6] R.P. Agarwal, M. Meehan, D. O'Regan, Fixed Point Theory and Applications, Cambridge University Press, Cambridge, 2001.
  • [7] R.R. Akhmerov, M.I. Kamenskii, A.S. Patapov, A.E. Rodkina, B.N. Sadovskii, Measures of Noncompactness and Condensing Operators, trans. from the Russian by A. Iacob, Birkhäuser Verlag, Basel, 1992.
  • [8] J.C. Alvàrez, Measure of noncompactness and fixed points of nonexpansive condensing mappings in locally convex spaces, Rev. Real. Acad. Cienc. Exact. Fis. Natur. Madrid 79 (1985) 53-66.
  • [9] J. Banaś, K. Goebel, Measures of Noncompactness in Banach Spaces, Marcel Dekker, New York, 1980.
  • [10] J. Banaś, B. Rzepka, An application of a measure of noncompactness in the study of asymptotic stability, Appl. Math. Lett. 16 (2003) 1-6.
  • [11] J. Banaś, K. Sadarangani, On some measures of noncompactness in the space of continuous functions, Nonlinear Anal. 68 (2008) 377-383.
  • [12] D.D. Bainov, P.S. Simeonov, Systems with Impulse Effect, Horwood, Chichester, 1989.
  • [13] M. Benchohra, J. Henderson, S.K. Ntouyas, Impulsive Differential Equations and Inclusions, Hindawi Publishing Corporation, Vol 2, New York, 2006.
  • [14] M. Benchohra, J. Henderson, D. Seba, Measure of noncompactness and fractional differential equations in Banach spaces, Commun. Appl. Anal. 12 (4) (2008) 419-428.
  • [15] D. Guo, V. Lakshmikantham, X. Liu, Nonlinear Integral Equations in Abstract Spaces, Kluwer Academic Publishers Group, Dordrecht, 1996.
  • [16] E. Hernández, D. O'Regan, On a new class of abstract impulsive differential equations, Proc. Amer. Math. Soc. 141 (2013) 1641-1649.
  • [17] R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000.
  • [18] A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier Science B.V., Amsterdam, 2006.
  • [19] V. Lakshmikantham, D.D. Bainov, P.S. Simeonov, Theory of Impulsive Differential Equations, Worlds Scientific, Singapore, 1989.
  • [20] H. Mönch, Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces, Nonlinear Anal. 4 (1980) 985-999.
  • [21] H. Mönch, G.F. Von Harten, On the Cauchy problem for ordinary differential equations in Banach spaces, Archiv. Math. Basel 39 (1982) 153-160.
  • [22] M. Pierri, D. O'Regan, V. Rolnik, Existence of solutions for semi-linear abstract differential equations with not instantaneous impulses, Appl. Math. Comput. 219 (2013) 6743-6749.
  • [23] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
  • [24] A.M. Samoilenko, N.A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore, 1995.
  • [25] Y. Zhou, Basic Theory of Fractional Differential Equations, World Scientific, Singapore, 2014.
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-b46af3f9-4c4d-4dd0-9b01-4dcb91823c57
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