Abstract fractional difference inclusions

Cover Page

Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription Access

Abstract

In this paper, we consider various classes of the abstract fractional difference inclusions with Weyl fractional derivatives and Riemann–Liouville fractional derivatives. We also provide some new results about the well-posedness of abstract integer-order difference inclusions with Euler forward operators, paying a special attention to the analysis of the existence and uniqueness of
almost periodic and almost automorphic type solutions to abstract fractional difference inclusions.

About the authors

Marko Kostić

Faculty of Technical Sciences, University of Novi Sad, Novi Sad, Serbia

Email: marco.s@verat.net

Halis Can Koyuncuoğlu

Izmir Katip Celebi University, Department of Engineering Sciences, Izmir, Turkey

Email: haliscan.koyuncuoglu@ikcu.edu.tr

Daniel Velinov

Department for Mathematics and Informatics, Faculty of Civil Engineering, Ss. Cyril and Methodius University of Skopje,Skopje, N. Macedonia

Email: velinovd@gf.ukim.edu.mk

References

  1. L. Abadias, C. Lizama, “Almost automorphic mild solutions to fractional partial difference-differential equations”, Appl. Anal., 95:6 (2016), 1347–1369
  2. L. Abadias, C. Lizama, P. J. Miana, M. Pilar Velasco, “On well-posedness of vector-valued fractional differential-difference equations”, Discrete Cont. Dyn. Syst., 39:5 (2019), 2679–2708
  3. O. A. Almatroud, A. Hioual, A. Ouannas, G. Grassi, “On fractional-order discrete-time reaction diffusion systems”, Mathematics, 11:11 (2023), 2447, 16 pp.
  4. E. Alvarez, S. Diaz, C. Lizama, “Existence of $(N,lambda)$-periodic solutions for abstract fractional difference equations”, Mediterr. J. Math., 19:1 (2022), 47, 15 pp.
  5. D. Araya, R. Castro, C. Lizama, “Almost automorphic solutions of difference equations”, Adv. Difference Equ., 2009 (2009), 591380, 15 pp.
  6. F. M. Atici, P. W. Eloe, “Initial value problems in discrete fractional calculus”, Proc. Amer. Math. Soc., 137:3 (2009), 981–989
  7. F. M. Atici, P. W. Eloe, “Discrete fractional calculus with the nabla operator”, Electron. J. Qual. Theory Differ. Equ., 2009, Spec. ed. I (2009), 3, 12 pp.
  8. F. M. Atici, P. W. Eloe, “Two-point boundary value problems for finite fractional difference equations”, J. Difference Equ. Appl., 17:4 (2011), 445–456
  9. A. S. Besicovitch, Almost periodic functions, Dover Publications, Inc., New York, 1955, xiii+180 pp.
  10. Junfei Cao, B. Samet, Yong Zhou, “Asymptotically almost periodic mild solutions to a class of Weyl-like fractional difference equations”, Adv. Difference Equ., 2019 (2019), 371, 33 pp.
  11. M. Choquehuanca, J. G. Mesquita, A. Pereira, “Almost automorphic solutions of second-order equations involving time scales with boundary conditions”, Proc. Amer. Math. Soc., 151:3 (2023), 1055–1070
  12. T. Diagana, Almost automorphic type and almost periodic type functions in abstract spaces, Springer, Cham, 2013, xiv+303 pp.
  13. A. Favini, A. Yagi, Degenerate differential equations in Banach spaces, Monogr. Textbooks Pure Appl. Math., 215, Marcel Dekker, Inc., New York, 1999, xii+313 pp.
  14. A. M. Fink, Almost periodic differential equations, Lecture Notes in Math., 377, Springer-Verlag, Berlin-New York, 1974, viii+336 pp.
  15. M. I. Gil', Difference equations in normed spaces. Stability and oscillations, North-Holland Math. Stud., 206, Elsevier Science B.V., Amsterdam, 2007, xvi+362 pp.
  16. C. Goodrich, A. C. Peterson, Discrete fractional calculus, Springer, Cham, 2015, xiii+556 pp.
  17. T. Hamadneh, A. Hioual,*O. Alsayyed, Y. A. Al-Khassawneh, A. Al-Husban, A. Ouannas, “The FitzHugh–Nagumo model described by fractional difference equations: stability and numerical simulation”, Axioms, 12:9 (2023), 806, 20 pp.
  18. Jia Wei He, C. Lizama, Yong Zhou, “The Cauchy problem for discrete time fractional evolution equations”, J. Comput. Appl. Math., 370 (2020), 112683, 15 pp.
  19. G. M. N'Guerekata, Almost automorphic and almost periodic functions in abstract spaces, Kluwer Acad. Publ., New York, 2001, x+138 pp.
  20. M. Kostic, Almost periodic and almost automorphic solutions to integro-differential equations, De Gruyter, Berlin, 2019, xli+329 pp.
  21. M. Kostic, Abstract degenerate Volterra integro-differential equations, Матем. ин-т САНУ, Београд, 2020, v+516 pp.
  22. M. Kostic, Selected topics in almost periodicity, De Gruyter Stud. Math., 84, De Gruyter, Berlin, 2022, xlviii+684 pp.
  23. M. Kostic, Metrical almost periodicity and applications to integro-differential equations, De Gruyter Stud. Math., 95, De Gruyter, Berlin, 2023, xxx+543 pp.
  24. M. Kostic, H. C. Koyuncuoğlu, “Multi-dimensional almost automorphic type sequences and applications”, Georgian Math. J., 31:3 (2024), 453–471
  25. C. Lizama, “The Poisson distribution, abstract fractional difference equations, and stability”, Proc. Amer. Math. Soc., 145:9 (2017), 3809–3827
  26. C. Lizama, M. Murillo-Arcila, C. Leal, “Lebesgue regularity for differential difference equations with fractional damping”, Math. Methods Appl. Sci., 41:7 (2018), 2535–2545
  27. S. Reich, I. Shafrir, “An existence theorem for a difference inclusion in general Banach spaces”, J. Math. Anal. Appl., 160:2 (1991), 406–412
  28. M. Vesely, Constructions of almost periodic sequences and functions and homogeneous linear difference and differential equations, PhD thesis, Masaryk Univ., Brno, 2011
  29. S. Zaidman, Almost-periodic functions in abstract spaces, Res. Notes in Math., 126, Pitman, Boston, MA, 1985, iii+133 pp.
  30. Shunian Zhang, “Almost periodic solutions of difference systems”, Chinese Sci. Bull., 43:24 (1998), 2041–2046
  31. Shunian Zhang, “Existence of almost periodic solutions for difference systems”, Ann. Differential Equations, 16:2 (2000), 184–206

Supplementary files

Supplementary Files
Action
1. JATS XML
Download

Copyright (c) 2025 Kostić M., Koyuncuoğlu H.C., Velinov D.

Согласие на обработку персональных данных

 

Используя сайт https://journals.rcsi.science, я (далее – «Пользователь» или «Субъект персональных данных») даю согласие на обработку персональных данных на этом сайте (текст Согласия) и на обработку персональных данных с помощью сервиса «Яндекс.Метрика» (текст Согласия).