Issue:Intuitionistic fuzzy Dirichlet problem

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Title of paper: Intuitionistic fuzzy Dirichlet problem Author(s): S. Melliani Department of Mathematics, Sultan Moulay Slimane University, BP 523, 23000, Beni Mellal, Morocco saidmelliani@gmail.com I. Bakhadach Department of Mathematics, Sultan Moulay Slimane University, BP 523, 23000, Beni Mellal, Morocco M. Elomari Department of Mathematics, Sultan Moulay Slimane University, BP 523, 23000, Beni Mellal, Morocco L. S. Chadli Department of Mathematics, Sultan Moulay Slimane University, BP 523, 23000, Beni Mellal, Morocco Published in: Notes on Intuitionistic Fuzzy Sets, Volume 24 (2018), Number 4, pages 72–84 DOI: https://doi.org/10.7546/nifs.2018.24.4.72-84 Download:  PDF (195 Kb  Kb, File info) Abstract: In the present paper, a new definition of intuitionistic fuzzy derivative is presented, which a generalization of fuzzy fractional derivative and is compatible with the “crisp” definition of fractional derivative. We prove some properties concerning this definition. Finally, the existence of Dirichlet problem is proven. Keywords: Hukuhara difference, Generalized intuitionistic fuzzy derivative, Intuitionistic fuzzy Caputo fractional derivative, Intuitionistic fuzzy Dirichlet problem. AMS Classification: 03E72, 34Gxx. References: Agarwal, R. P., Lakshmikantham, V., Nieto, J. J. (2010). On the concept of solution for fractional differential equations with uncertainty, Nonlinear Anal., 72(6), 2859–2862. Allahviranloo, T., Armand, A., & Gouyandeh, Z. (2014). Fuzzy fractional differential equations under generalized fuzzy Caputo derivative, J. Intelligent and Fuzzy Systems, 26, 1481– 1490. Arara, A., Benchohra, M., Hamidi, N., & Nieto, J. J. (2010). Fractional order differential equations on an unbounded domain, Nonlinear Anal., 72(2), 580–586. Atanassov, K. (1983). Intuitionistic fuzzy sets, VII ITKR Session, Sofia, 20-23 June 1983 (Deposed in Centr. Sci.-Techn. Library of the Bulg. Acad. of Sci., 1697/84) (in Bulgarian). Reprinted: Int. J. Bioautomation, 2016, 20(S1), S1–S6. Atanassov, K. (1986). Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1), 87–96. Bede, B., & Stefanini, L. (2013). Generalized differentiability of fuzzy-valued functions, Fuzzy Sets and Systems, 230, 119–141. De Luca, A., & Termini, S. (1972). A definition of non Probabilistic entropy in the setting of fuzzy theory, Information and Control, 20(4), 301–312. Elomari, M., Melliani, S., & Chadli, L. S. (2017). Solution of intuitionistic fuzzy fractional differential equations. Annals of Fuzzy Mathematics and Informatics, 13(3), 379–391. Kilbas, A. A., Srivastava, H. M., & Trujillo, J. J. (2006). Theory and applications of fractional differential equations, Amesterdam: Elsevier Science. Melliani, S., Elomari, M., Chadli, L. S. & Ettoussi, R. (2015). Intuitionistic fuzzy metric space, Notes on Intuitionistic Fuzzy Sets, 21(1), 43–53. 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. Podlubny, I. (1999). Fractional Differential Equations, Academic Press, San Diego. Stefanini, L., & B. Bede, (2009). Generalized hukuhara differentiability of interval-valued functions and interval differential equations, Nonlinear Analysis: Theory, Methods and Applications 71(34), 1311–1328. Zadeh, L. A. (1965). Fuzzy sets, Information and Control, 8, 338–353. Citations: Issue:Intuitionistic fuzzy evolution problem with nonlocal conditions ‎ (← links) The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.