Complex Fuzzy Evolution Equation with Nonlocal Conditions
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Complex Fuzzy Evolution Equation with Nonlocal Conditions

Authors: Abdelati El Allaoui, Said Melliani, Lalla Saadia Chadli


The objective of this paper is to study the existence and uniqueness of Mild solutions for a complex fuzzy evolution equation with nonlocal conditions that accommodates the notion of fuzzy sets defined by complex-valued membership functions. We first propose definition of complex fuzzy strongly continuous semigroups. We then give existence and uniqueness result relevant to the complex fuzzy evolution equation.

Keywords: Complex fuzzy evolution equations, nonlocal conditions, mild solution, complex fuzzy semigroups.

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[1] R. F. Arens, J. Eells, On embedding uniform and topological spaces, Pac. J. Math. 6 (1956) 397–403.
[2] Daria Karpenko, Robert A. Van Gorder, Abraham Kandel, The Cauchy problem for complex fuzzy differential equations, Fuzzy Sets and Systems 245 (2014) 18-29.
[3] A. El Allaoui, S. Melliani and L. S. Chadli, Fuzzy dynamical systems and Invariant attractor sets for fuzzy strongly continuous semigroups, Journal of Fuzzy Set Valued Analysis 2016 No.2 (2016) 148–155.
[4] K. Ezzinbi and James H. Liu, Nondensely Defined Evolution Equations with Nonlocal Conditions, Mathematical and Computer Modelling 36 (2002) 1027–1038.
[5] M. Hukuhara, Integration des applications measurables dont la valeur est un compact convexe, Funk. Ekvacioj. 10 (1967) 207–223.
[6] O. Kaleva. Fuzzy Diferentiel Equations, Fuzzy Sets and Systems. 24 (1987) 301–317.
[7] S. Melliani, A. El Allaoui and L. S. Chadli, Relation Between Fuzzy Semigroups and Fuzzy Dynamical Systems, Nonlinear Dynamics and Systems Theory, 17 (1) (2017) 60–69.
[8] J. Nieto, The Cauchy problem for continuous fuzzy differential equations, Fuzzy Sets Syst. 102 (1999) 259-262.
[9] M. L. Puri, D. A. Ralescu. Fuzzy random variables, J. Math. Anal. Appl. 114 (1986) 409–422.
[10] Daniel Ramot, Ron Milo, Menahem Friedman, and Abraham Kandel, Complex Fuzzy Sets, IEEE Transactions on Fuzzy Systems, 10 (2002).
[11] D. E. Tamir, L. Jin, A. Kandel, A new interpretation of complex membership grade, Int. J. Intell. Syst. 26 (2011) 285-312.