Research article

Measure pseudo almost automorphic solution to second order fractional impulsive neutral differential equation

  • Received: 18 November 2020 Accepted: 12 May 2021 Published: 31 May 2021
  • MSC : 12H20, 34A08, 47G20, 34A37, 43A60

  • We discuss the concept of pseudo almost automorphic solution to fractional neutral differential equation with impulses using measure theory. Our principal results are obtained via semigroup theory and the fixed point theorem due to Krasnoselskii and their combination with the properties of measure theory. An example is provided to outline the thought developed on this work.

    Citation: Velusamy Kavitha, Dumitru Baleanu, Jeyakumar Grayna. Measure pseudo almost automorphic solution to second order fractional impulsive neutral differential equation[J]. AIMS Mathematics, 2021, 6(8): 8352-8366. doi: 10.3934/math.2021484

    Related Papers:

  • We discuss the concept of pseudo almost automorphic solution to fractional neutral differential equation with impulses using measure theory. Our principal results are obtained via semigroup theory and the fixed point theorem due to Krasnoselskii and their combination with the properties of measure theory. An example is provided to outline the thought developed on this work.



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    [1] S. Abbas, L. Mahto, M. Hafayed, A. M. Alimi, Asymptotic almost automorphic solutions of impulsive neural network with almost automorphic coefficients, Neurocomputing, 142 (2014), 326–334. doi: 10.1016/j.neucom.2014.04.028
    [2] S. Abbas, V. Kavitha, R. Murugesu, Stepanov-like weighted pseudo almost automorphic solutions to fractional order abstract integro-differential equations, P. Indian AS-Math. Sci., 125 (2015), 323–351. doi: 10.1007/s12044-015-0235-6
    [3] D. D. Bainov, P. S. Simeonov, Impulsive Differential Equations: Asymptotic Properties of the Solutions, World Scientific Singapore, 1995.
    [4] J. Blot, G. M. Mophou, G. M. N'Guérékata, D. Pennequin, Weighted pseudo almost automorphic functions and applications to abstract differential equations, Nonlinear Anal., 71 (2009), 903–909. doi: 10.1016/j.na.2008.10.113
    [5] J. Blot, P. Cieutat, K. Ezzinbi, Measure theory and pseudo almost automorphic functions: New developments and applications, Nonlinear Anal,, 75 (2012), 2426–2447.
    [6] S. Bochner, Continuous mappings of almost automorphic and almost periodic functions, P. Natl. A. Sci. India. B., 52 (1964), 907–910. doi: 10.1073/pnas.52.4.907
    [7] H. Bohr, Almost-Periodic Functions, Chelsea, reprint, 1947.
    [8] Y. K. Chang, M. M. Arjunan, G. M. N'Guérékata, V. Kavitha, On global solutions to fractional functional differential equations with infinite delay in Fréchet spaces, Comput. Math. Appl., 62 (2011), 1228–1237. doi: 10.1016/j.camwa.2011.03.039
    [9] Y. K. Chang, X. X. Luo, Existence of $\mu$-pseudo almost automorphic solutions to a neutral differential equation by interpolation theory, Filomat, 28 (2014), 603–614. doi: 10.2298/FIL1403603C
    [10] Y. K. Chang, G. M. N'Guérékata, R. Zhang, Stepanov-like weighted pseudo almost automorphic functions via measure theory, B. Malays. Math. Sci. So., 3 (2015), 1005–1041.
    [11] Y. K. Chang, T. W. Feng, Properties on measure pseudo almost automorphic functions and applications to fractional differential equations in Banach spaces, Electronic J. Differ. Eq., 2018 (2018), 1–14. doi: 10.1186/s13662-017-1452-3
    [12] P. Chen, X. Zhang, Y. Li, Non-autonomous parabolic evolution equations with non-instantaneous impulses governed by noncompact evolution families, J. Fixed Point Theory Appl., 21 (2019). Available from: https://doi.org/10.1007/s11784-019-0719-6.
    [13] P. Chen, X. Zhang, Y. Li, Non-autonomous evolution equations of parabolic type with non-instantaneous impulses, Mediterr. J. Math., 16 (2019). Available from: https://doi.org/10.1007/s00009-019-1348-0.
    [14] P. Chen, X. Zhang, Y. Li, Fractional non-autonomous evolution equation with nonlocal conditions, J. Pseudo-Differ. Oper., 10 (2019), 955–973. doi: 10.1007/s11868-018-0257-9
    [15] P. Chen, X. Zhang, Y. Li, Cauchy problem for fractional non-autonomous evolution equations, Banach J. Math. Anal., 14 (2020), 559–584. doi: 10.1007/s43037-019-00008-2
    [16] P. Chen, X. Zhang, Y. Li, Existence and approximate controllability of fractional evolution equations with nonlocal conditions via resolvent operators, Frac. Calc. Appl. Anal., 23 (2020), 268–291. doi: 10.1515/fca-2020-0011
    [17] P. Chen, X. Zhang, Y. Li, Approximate controllability of non-autonomous evolution system with nonlocal conditions, J. Dyn. Control Syst., 26 (2020), 1–16. doi: 10.1007/s10883-018-9423-x
    [18] A. M. Samoilenko, N. A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore, 1995.
    [19] E. Cuesta, Asymptotic bahaviour of the solutions of fractional integrodifferential equations and some time discretizations, Discrete Continuum Dynamics Systems(Supplement) (2007), 277–285.
    [20] K. Diethelm, The Analysis of Fractional Differential Equations, Springer, New York, 2010.
    [21] V. Kavitha, S. Abbas, R. Murugesu, ($\mu_1, \mu_2$)-pseudo almost automorphic solutions of fractional order neutral integro-differential equations, Nonlinear Studies, 24 (2017), 669–685.
    [22] M. A. Krasnoselskii, P. P. Zabreiko, Geometrical Methods of Nonlinear Analysis, Springer, Berlin, 1984.
    [23] M. Lakshman, S. Abbas, PC-almost automorphic solution of impulsive fractional differential equations, Mediterr. J. Math., 12 (2015), 771–790. doi: 10.1007/s00009-014-0449-3
    [24] V. D. Milman, A. D. Myshkis, On the stability of motion in the presence of impulses (in Russian), Siberian Math. J., 1 (1960), 233–237.
    [25] C. Wang, R. P Agarwal, Weighted piecewise pseudo almost automorphic functions with applications to abstract impulsive $\nabla$-dynamic equations on time scales, Advances in Difference Equations, (2014). Available from: https://doi.org/10.1186/1687-1847-2014-153.
    [26] Z. Xia, D. Wang, Measure pseudo almost periodic mild solutions of stochastic functional differential equations with Levy noise, J. Nonlinear Convex A., 18 (2017), 847–858.
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