Issue:Intuitionistic fuzzy fractional equation

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Title of paper: Intuitionistic fuzzy fractional equation Author(s): Said Melliani Laboratoire de Mathématiques Appliquées & Calcul Scientifique, Sultan Moulay Slimane University, BP 523, 23000 Beni Mellal, Morocco said.melliani@gmail.com M'hamed Elomari Laboratoire de Mathématiques Appliquées & Calcul Scientifique, Sultan Moulay Slimane University, BP 523, 23000 Beni Mellal, Morocco Lalla Saadia Chadli Laboratoire de Mathématiques Appliquées & Calcul Scientifique, Sultan Moulay Slimane University, BP 523, 23000 Beni Mellal, Morocco Razika Ettoussi Laboratoire de Mathématiques Appliquées & Calcul Scientifique, Sultan Moulay Slimane University, BP 523, 23000 Beni Mellal, Morocco Published in: "Notes on Intuitionistic Fuzzy Sets", Volume 21, 2015, Number 4, pages 76–89 Download:  PDF (228  Kb, File info) Abstract: In this paper, we discuss the existence and uniqueness of mild solution for intuitionistic fuzzy fractional equation using the concept of semigroup in the intuitionistic fuzzy theory and the theorem of fixed point in the complete metric space. Keywords: Intuitionistic fuzzy fractional equation, Metric space. AMS Classification: 03E72, 08A72. References: Allahviranloo, T. & M. B. Ahmadi (2010) Fuzzy Laplace transforms, Soft Computing, 14, 235–243. Bede, B. & S. G. Gal (2005) Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations, Fuzzy Sets and Systems, 151, 581–599. Diamond, P. & P. E. Kloeden (1994) Metric Spaces of Fuzzy Sets, World Scientific, Singapore. Gal, C. G. & S. G. Gal (2013) Semigroups of Operators on Spaces of Fuzzy-Number-Valued Functions with Applications to Fuzzy Differential Equations, arXiv:1306.3928v1, 17 June 2013. Gelfand, I. M. & G. E. Shilvoe (1958) Generalized Functions, Vol. 1, Moscow. O. Kaleva (2006) A note on fuzzy differential equations. Nonlinear Analysis, 64, 895–900. Kilbas, A. A., H. M. Srivastava & J. J. Trujillo (2006) Theory and Applications of Fractional Differential Equations, Elsevier Science B.V, Amsterdam. Klement, E. P., M. L. Puri & D. A. Ralescu (1986) Limit Theorems for Fuzzy Random Variables, Proc. R. Soc. Lond. A, 407, 171-182. Lakshmikantham, V. & R. N. Mohapatra (2003) Theory of Fuzzy Differential Equations and Applications, Taylor and Francis, London. Lakshmikantham, V. & A. S. Vatsala (2008) Basic theory of fractional differential equations, Nonlinear Anal., 69, 2677–2682. Laksmikantham, V. & S. Leela (2009) Nagumo-type uniqueness result for fractional differential equations, Nonlinear Anal., 8, 2886–2889. Melliani, S., M. Elomari, L. S. Chadli & R. Ettoussi (2015) Intuitionistic fuzzy metric space, Notes on Intuitionistic Fuzzy Sets, 21(1), 43–53. Melliani, S., M. Elomari, L. S. Chadli & R. Ettoussi (2015) Intuitionistic fuzzy semigroup, Notes on Intuitionistic Fuzzy Sets, 21(2), 43–50. Oldham, K. B. & J. Spanier (1974) The Fractional Calculus, Academic Press, New York. Samko, S. G., A. A. Kilbas & O. I. Marichev (1993) Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach Sci. Publishers, London-New York. Shilove, G. E. (1968) Generalized functions and partial differential equations, Mathematics and Its Applications, Science publishers, Inc.. Shuqin, Z. (2009) Monotone iterative method for initial value problem involving Riemann-Liouville fractional derivatives, Nonlinear Anal., 71, 2087–2093. Citations: Issue:The Cauchy problem for intuitionistic fuzzy differential equations ‎ (← links) Issue:Solution of n-th order intuitionistic fuzzy differential equation by variational iteration method ‎ (← links) Issue:Stability of intuitionistic fuzzy nonlinear fractional differential equations ‎ (← links) 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.