| Title of paper:
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Intuitionistic fuzzy Dirichlet problem
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| Author(s):
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| S. Melliani
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| Department of Mathematics, Sultan Moulay Slimane University, BP 523, 23000, Beni Mellal, Morocco
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| saidmelliani@gmail.com
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| I. Bakhadach
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| Department of Mathematics, Sultan Moulay Slimane University, BP 523, 23000, Beni Mellal, Morocco
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| M. Elomari
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| Department of Mathematics, Sultan Moulay Slimane University, BP 523, 23000, Beni Mellal, Morocco
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| L. S. Chadli
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| Department of Mathematics, Sultan Moulay Slimane University, BP 523, 23000, Beni Mellal, Morocco
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| Published in:
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Notes on Intuitionistic Fuzzy Sets, Volume 24 (2018), Number 4, pages 72–84
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| DOI:
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https://doi.org/10.7546/nifs.2018.24.4.72-84
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| Download:
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 PDF (195 Kb Kb, Info)
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| Abstract:
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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.
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| Keywords:
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Hukuhara difference, Generalized intuitionistic fuzzy derivative, Intuitionistic fuzzy Caputo fractional derivative, Intuitionistic fuzzy Dirichlet problem.
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| AMS Classification:
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03E72, 34Gxx.
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| References:
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- 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.
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