As of August 2024, International Journal "Notes on Intuitionistic Fuzzy Sets" is being indexed in Scopus.
Please check our Instructions to Authors and send your manuscripts to nifs.journal@gmail.com. Next issue: September/October 2024.
Open Call for Papers: International Workshop on Intuitionistic Fuzzy Sets • 13 December 2024 • Banska Bystrica, Slovakia/ online (hybrid mode).
Deadline for submissions: 16 November 2024.

Issue:Stability of intuitionistic fuzzy nonlinear fractional differential equations

From Ifigenia, the wiki for intuitionistic fuzzy sets and generalized nets
Jump to navigation Jump to search
shortcut
http://ifigenia.org/wiki/issue:nifs/27/1/83-100
Title of paper: Stability of intuitionistic fuzzy nonlinear fractional differential equations
Author(s):
Said Melliani
LMACS, Sultan Moulay Slimane University, BP 523, 23000, Beni Mellal, Morocco
s.melliani@usms.ma
Ali El Mfadel
LMACS, Sultan Moulay Slimane University, BP 523, 23000, Beni Mellal, Morocco
elmfadelali@gmail.com
Lalla Saadia Chadli
LMACS, Sultan Moulay Slimane University, BP 523, 23000, Beni Mellal, Morocco
sa.chadli@yahoo.fr
M'hamed Elomari
LMACS, Sultan Moulay Slimane University, BP 523, 23000, Beni Mellal, Morocco
m.elomari@usms.ma
Published in: Notes on Intuitionistic Fuzzy Sets, Volume 27 (2021), Number 1, pages 83–100
DOI: https://doi.org/10.7546/nifs.2021.27.1.83-100
Download:  PDF (301  Kb, File info)
Abstract: In this paper, we study the existence and uniqueness results of solution for the intuitionistic fuzzy nonlinear fractional differential equations involving the Caputo concepts of fractional derivative. In addition, we establish essentially the Mittag-Leffler stability result for the intuitionistic fuzzy nonlinear fractional differential equations by giving some sufficient criteria to guarantee the stability of the zero solution. Finally, some examples are presented to illustrate the proposed stability theorem.
Keywords: Intuitionistic fuzzy numbers, Intuitionistic fuzzy fractional integral, Intuitionistic fuzzy fractional Caputo derivative, Mittag-Leffler stability
AMS Classification: 34A07
References:
  1. Agarwal, R. P., Lakshmikantham, V., & Nieto, J. J. (2010). On the concept of solution for fractional differential equations with uncertainty. Nonlinear Analysis: Theory, Methods & Applications, 72(6), 2859–2862.
  2. Agarwal, R., O’Regan, D., & Hristova, S. (2015). Stability of Caputo fractional differential equations by Lyapunov functions. Applications of Mathematics, 60, 653–676.
  3. Alikhani, R., & Bahrami, F. (2013). Global solutions for nonlinear fuzzy fractional integral and integrodifferential equations. Communications in Nonlinear Science and Numerical Simulation, 18(8), 2007–2017.
  4. Allahviranloo, T., Armand, A., & Gouyandeh, Z. (2014). Fuzzy fractional differential equations under generalized fuzzy Caputo derivative. Journal of Intelligent and Fuzzy Systems, 26(3), 1481–1490.
  5. Arshad, S., & Lupulescu, V. (2011). On the fractional differential equations with uncertainty. Nonlinear Analysis: Theory, Methods & Applications, 74(11), 3685–3693.
  6. Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87–96.
  7. Bede, B. (2005). Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations. Fuzzy Sets and Systems, 151(3), 581–599.
  8. Burton, T. A., & Zhang, B. (2012). Fractional equations and generalizations of Schaefer’s and Krasnoselskii’s fixed point theorems. Nonlinear Analysis: Theory, Methods & Applications, 75(18), 6485–6495.
  9. Diethelm, K., & Ford, N. J. (2002). Analysis of fractional differential equations. Journal of Mathematical Analysis and Applications, 265(2), 229–248.
  10. Elomari, M., Melliani, S., & Chadli, L. S. (2016). Solution of intuitionistic fuzzy fractional differential equations. Annals of Fuzzy Mathematics and Informatics, 13(3), 379–391.
  11. Hoa, N. V., Lupulescu, V., & O’Regan, D. (2018). A note on initial value problems for fractional fuzzy differential equations. Fuzzy Sets and Systems, 347, 54–69.
  12. Kilbas, A., Srivastava, M., & Trujillo, J. (2006). Theory and Applications of Fractional Differential Equations. North-Holland Mathematical Studies, Vol. 204, Ed van Mill, Amsterdam.
  13. Li, C. P., Zhang, F. R. (2011). A survey on the stability of fractional differential equations. The European Physical Journal Special Topics, 193, 27–47.
  14. Li, Y., Chen, Y. Q., & Podlubny, I. (2009). Mittag-Leffler stability of fractional order nonlinear dynamic systems. Automatica, 45, 1965–1969.
  15. Li, Y., Chen, Y., & Podlubny, I. (2010). Lyapunov direct method and generalized Mittag-Leffler stability. Computers & Mathematics with Applications, 59(5), 1810–1821.
  16. Liu, K. W., & Jiang, W. (2011). Finite-time stability of linear fractional order neutral systems. Mathematica Applicata, 24, 724–730.
  17. Matignon, D. (1996). Stability results for fractional differential equations with applications to control processing. In: IMACS-SMC, Lille, France, 963–968.
  18. Melliani, S., Elomari, M., Chadli, L.S., & Ettoussi, R. (2015). Extension of Hukuhara difference in intuitionistic fuzzy set theory. Notes on Intuitionistic Fuzzy Sets, 21(4), 34–47.
  19. Melliani, S., Elomari, M., Chadli, L.S., & Ettoussi, R. (2015). Intuitionistic fuzzy fractional equation. Notes on Intuitionistic Fuzzy Sets, 21(4), 76–89.
  20. Momani, S., & Hadid, S. (2004). Lyapunov stability solutions of fractional integrodifferential equations. International Journal of Mathematics and Mathematical Sciences, 47, Article ID 575670, 2503–2507.
  21. Salahshour, S., Allahviranloo, T., Abbasbandy, S., & Baleanu, D. (2012). Existence and uniqueness results for fractional differential equations with uncertainty. Advances in Difference Equations, 2012, Art. No. 112.
  22. Schauder, J. (1930). Der Fixpunktsatz in Funktionalraumen, ¨ Studia Mathematica, 2(1), 171–180.
  23. Schwartz, L. (1997). Analyse I, Theorie des Ensembles et Topologie, Hermann Editeurs, Paris, pp. 346.
  24. Weissinger, J. (1952). Zur Theorie und Anwendung des Iterationsverfahrens. Mathematische Nachrichten, 8(1), 193–212.
  25. Xu, Z. S., & Yager, R. R. (2006). Some geometric aggregation operators based on intuitionistic fuzzy sets. International Journal of General Systems, 35(4), 417–433.
  26. Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–356.
Citations:

The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.

Retrieved from "https://ifigenia.org/index.php?title=Issue:Stability_of_intuitionistic_fuzzy_nonlinear_fractional_differential_equations&oldid=13598"