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Existence and attractivity results on semi-infinite intervals for integrodifferential equations with non-instantaneous impulsions in Banach spaces Cover

Existence and attractivity results on semi-infinite intervals for integrodifferential equations with non-instantaneous impulsions in Banach spaces

Open Access
|May 2024

References

  1. S. Abbas and M. Benchohra, Advanced Functional Evolution Equations and Inclusions, Developments in Mathematics, 39. Springer, Cham, 2015.
  2. S. Abbas, M. Benchohra, G. M. N’Guérékata, Instantaneous and noninstantaneous impulsive integrodi erential equations in Banach spaces, J. Anal. Appl. 38 (2) (2020), 143–156.
  3. R. S. Adiguzel, U. Aksoy, E. Karapinar, I. M. Erhan, On the solution of a boundary value problem associated with a fractional differential equation. Math. Meth. Appl. Sci. (2020), 112.
  4. R. S. Adiguzel, U. Aksoy, E. Karapinar, I. M. Erhan, Uniqueness of solution for higher-order nonlinear fractional differential equations with multi-point and integral boundary conditions. Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. RACSAM 115 (2021), 115155.
  5. R. S. Adiguzel, U. Aksoy, E. Karapinar, I. M. Erhan, On the solutions of fractional differential equations via Geraghty type hybrid contractions. Appl. Comput. Math. 20 (2021), 313–333.
  6. H. Afshari and E. Karapinar, A solution of the fractional differential equations in the setting of b-metric space. Carpathian Math. Publ. 13 (2021), 764–774. https://doi.org/10.15330/cmp.13.3.764–774
  7. H. Afshari and E. Karapinar, A discussion on the existence of positive solutions of the boundary value problems via ψ-Hilfer fractional derivative on b-metric spaces. Adv. Difference Equ. 2020 (2020), 616. https://doi.org/10.1186/s13662-020-03076-z
  8. R. P. Agarwal and D. O’Regan, Infinite Interval Problems for Differntial, Difference and Integral Equation, Academic Publishers, Dordrecht, 2001.
  9. R. P. Agarwal and D. O’Regan, Infinite interval problems modeling phenomena which arise in the theory of plasma and electrical potential theory, Stud. Appl. Math. 111 (2003), 339–358.
  10. D. D. Bainov and P. S. Simeonov, Systems with Impulse Effect: Theory and Applications, Ellis Horwood, Chichister, 1989.
  11. J. Banaś, K. Goebel: Measure of Noncompactness in Banach Spaces. in: Lecture Notes in Pure and Applied Math, 60, Marcel Dekker, New York, 1980.
  12. J. Banaś, Measures of noncompactness in the space of continuous tempered functions, Demonstr. Math. 14 (1981), 127–133.
  13. A. Belleni-Morante, An integrodifferential equation arising from the theory of heat conduction in rigid material with memory, Boll. Un. Mat. Ital. 15 (1978), 470–482.
  14. M. Benchohra, F. Bouazzaoui, E. Karapinar and A. Salim, Controllability of second order functional random differential equations with delay. Math. 10 (2022), 16 pp. https://doi.org/10.3390/math10071120
  15. M. Benchohra, J. Henderson and S. K. Ntouyas, Impulsive Differential Equations and inclusions, Hindawi Publishing Corporation, New York, 2006.
  16. M. Benchohra, N. Rezoug, Existence and Attractivity of Solutions of Semilinear Volterra Type Integro-Differential Evolution Equations, Surv. Math. Appl. 13 (2018), 215–235.
  17. N. Benkhettou, K. Aissani, A. Salim, M. Benchohra and C. Tunc, Controllability of fractional integro-differential equations with infinite delay and non-instantaneous impulses, Appl. Anal. Optim. 6 (2022), 79–94.
  18. J. Blot, C. Buse, P. Cieutat, Local attractivity in nonautonomous semi-linear evolution equations. Nonauton. Dyn. Syst. 1 (2014), 72–82.
  19. L. Byszewski, Application of properties of the right-hand sides of evolution equations to an investigation of nonlocal evolution problems, Nonl. Anal. 33 (1998), 413–426.
  20. L. Byszewski, Existence and uniqueness of a classical solution to a functional-differential abstract nonlocal Cauchy problem. Appl. Math. Stoch. Anal. 12 (1999), 91–97.
  21. L. Byszewski and V. Lakshmikantham, Theorem about the existence and uniqueness of a solution of a nonlocal abstract Cauchy problem in a Banach space, Appl. Anal. 40 (1990), 11–19.
  22. W. Desch, R. C. Grimmer and W. Schappacher, Some considerations for linear integrodiffferential equations, J. Math. Anal. Appl. 104 (1984), 219–234.
  23. M. A. Diop, K. Ezzinbi, M. P. Ly, Nonlocal problems for integrodifferential equation via resolvent operators and optimal control, Discuss. Math. Differ. Incl. Control Optim. 42 (2022), 5–25.
  24. B.C. Dhage, V. Lakshmikantham, On global existence and attractivity results for nonlinear functional integral equations, Nonlinear Anal. 72 (2010) 2219–2227
  25. S. Dudek and L. Olszowy, Continuous dependence of the solutions of nonlinear integral quadratic Volterra equation on the parameter. J. Funct. Spaces 2015, Art. ID 471–235, 9 pp.
  26. J. Dugundji, A. Granas, Fixed Point Theory, Springer-Verlag, New York, 2003.
  27. R. C. Grimmer, Resolvent opeators for integral equations in a Banach space, Trans. Amer. Math. Soc. 273 (1982), 333–349.
  28. R. C. Grimmer and A. J. Pritchard, Analytic resolvent operators for integral equations in a Banach space, J. Differential Equations 50 (1983), 234–259.
  29. X. Hao, L. Liu, Mild solution of semilinear impulsive integro-differential evolution equation in Banach spaces . Math. Methods Appl. Sci. 40 (13) (2017), 4832–4841.
  30. A. Heris, A. Salim, M. Benchohra and E. Karapinar, Fractional partial random differential equations with infinite delay. Results in Physics. (2022). https://doi.org/10.1016/j.rinp.2022.105557
  31. E. Hernàndez, D. O’Regan, On a new class of abstract impulsive differential equations, Proc. Amer. Math. Soc. 141 (2013), no. 5, 1641–1649.
  32. A. Jawahdou, Mild solutions of functional semilinear evolution Volterra integrodifferential equations on an unbounded interval, Nonlinear Anal. 74 (2011), 7325–7332
  33. N. N. Krylov and N. N. Bogolyubov, Introduction to Nonlinear Mechanics, Izd. Acad. Sci. Ukr. SSR, Kiev, 1937.
  34. R. R. Kumar, Nonlocal Cauchy problem for analytic resolvent operator integrodifferential equations in Banach spaces, Appl. Math. Comput. 204 (2008), 352–362.
  35. R. R. Kumar, Regularity of solutions of evolution integrodifferential equations with deviating argument, Appl. Math. Comput. 217 (2011), 9111–9121.
  36. V. Lakshmikantham, D. D. Bainov, and P. S. Simeonov, Theory of Impulsive Differential Equations, Series in Modern Applied Mathematics, 6, World Scientific, New Jersey, 1989.
  37. J. Mikusiéski, The Bochner Integral, Birkhuser, Basel, 1978.
  38. L. Olszowy and S. Wedrychowicz, Mild solutions of semilinear evolution equation on an unbounded interval and their applications. Nonlinear Anal. 72 (2010), no. 3–4, 2119–2126.
  39. A. Salim, S. Abbas, M. Benchohra and E. Karapinar, Global stability results for Volterra-Hadamard random partial fractional integral equations. Rend. Circ. Mat. Palermo (2). (2022), 1–13. https://doi.org/10.1007/s12215-022-00770-7
  40. J. M. A. Toledano, T. Dominguez Benavides and G. Lopez Acedo, Measures of Noncompactness in Metric Fixed Point Theory, Adv. Oper. Theory. 99, Birkhauser, Basel, Boston, Berlin, 1997.
  41. K. Yosida, Functional Analysis 6 Springer-Verlag, Berlin, 1980.
DOI: https://doi.org/10.2478/auom-2024-0004 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784
Language: English
Page range: 65 - 84
Submitted on: Oct 6, 2022
Accepted on: Feb 7, 2023
Published on: May 27, 2024
Published by: Ovidius University of Constanta
In partnership with: Paradigm Publishing Services
Publication frequency: 3 issues per year

© 2024 Abdelhamid Bensalem, Abdelkrim Salim, Mouffak Benchohra, Erdal Karapinar, published by Ovidius University of Constanta
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