Abstract
This paper investigates the existence to the impulsive fuzzy evolution equation via fixed point theorem for absolute retract, take into consideration that \(E^n\) can be embedded isomorphically as a cone in a Banach space.
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Agarwal, R.P., Benchohra, M., O’Regan, D., Ouahab, A.: Fuzzy solutions for multi-point boundary value problems. Mem. Differ. Equ. Math. Phys. 35, 1–14 (2005)
Agarwal, R.P., O’Regan, D., Lakshmikantham, V.: Viability theory and fuzzy differential equations. Fuzzy Sets Syst. 151, 563–580 (2005)
Agarwal, R.P., O’Regan, D., Lakshmikantham, V.: A stacking theorem approach for fuzzy differential equations. Nonlinear Anal. 55, 299–312 (2003)
Aumann, R.J.: Integrals of set-valued functions. J. Math. Anal. Appl. 12, 1–12 (1965)
Benchohra, M., Nieto, J.J., Ouahab, A.: Fuzzy solutions for impulsive differential equations. Commun. Appl. Anal. 11, 379–394 (2007)
Diamond, P., Kloeden, P.E.: Metric Spaces of Fuzzy Sets: Theory and Applications. World Scientific, Singapore (1994)
El Allaoui, A., Melliani, S., Chadli, L.S.: Fuzzy dynamical systems and Invariant attractor sets for fuzzy strongly continuous semigroups. J. Fuzzy Set Valued Anal. 2, 148–155 (2016)
El Allaoui, A., Melliani, S., Chadli, L.S.: Fuzzy \(\alpha -\)semigroups of operators. Gen. Lett. Math. 2(2), 42–49 (2017)
Gal, C.G., Gal, S.G.: Semigroups of Operators on Spaces of Fuzzy-Number-Valued Functions with Applications to Fuzzy Differential Equations, vol. 17 (2013). arXiv:1306.3928v1
Granas, A., Dugundji, J.: Fixed Point Theory. Springer, New York (2003)
Kaleva, Osmo: Nonlinear iteration semigroups of fuzzy Cauchy problems. Fuzzy Sets Syst. 209, 104–110 (2012)
Kim, Y.K.: Measurability for fuzzy valued functions. Fuzzy Sets Syst. 129, 105–109 (2002)
Klement, E., Puri, M., Ralescu, D.: Limit theorems for fuzzy random variables. Proc. Roy. Soc. Lond. Ser. A 407, 171–182 (1986)
Lakshmikantham, V., Mcrae, F.A.: Basic results for impulsive fuzzy differential equations. Math. Inequal. Appl. 4, 239–246 (2001)
Melliani, S., Chadli, L.S., El Allaoui, A.: Periodic boundary value problems for controlled nonlinear impulsive evolution equations on Banach spaces. Int. J. Nonlinear Anal. Appl. 8(1), 301–314 (2017). https://doi.org/10.22075/ij-naa.2017.1460.1370
Melliani, S., El Allaoui, A., Chadli, L.S.: A general class of periodic boundary value problems for controlled nonlinear impulsive evolution equations on Banach spaces. Adv. Differ. Equ. 2016, 290 (2016). https://doi.org/10.1186/s13662-016-1004-2
Melliani, S., El Allaoui, A., Chadli, L.S.: Relation between fuzzy semigroups and fuzzy dynamical systems. Nonlinear Dyn. Syst. Theory 17(1), 60–69 (2017)
Melliani, S., Eljaoui, E.H., Chadli, L.S.: Fuzzy differential equation with nonlocal conditions and fuzzy semigroups. Advances in Difference Equations, p. 35 (2016)
Nieto, J.J., Rodriguez-Lopez, R., Villanueva-Pesqueira, M.: Exact solution to the periodic boundary value problem for a first-order linear fuzzy differential equation with impulses. Fuzzy Optim. Decis. Making 10, 323–339 (2011)
Pazy, A.: Semigroups of Linear Operators and Applications to Partiel Differential Equations. Springer, New York (1983)
Puri, M., Ralescu, D.: Fuzzy random variables. J. Math. Anal. Appl. 114, 409–422 (1986)
Puri, M., Ralescu, D.: The concept of normality for fuzzy random variables. Ann. Probab. 13, 1373–1379 (1985)
Puri, M., Ralescu, D.: Convergence theorem for fuzzy martingales. J. Math. Anal. Appl. 160, 107–122 (1991)
Rodriguez-Lopez, Rosana: Periodic boundary value problems for impulsive fuzzy differential equations. Fuzzy Sets Syst. 159, 1384–1409 (2008)
Vatsala, A.S.: Impulsive hybrid fuzzy differential equations. FACTA UNI-VERSITATIS Ser.: Mech. Autom. Control Robot. 3, 851–859 (2003)
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The authors express their sincere thanks to the anonymous referees for numerous helpful and constructive suggestions which have improved the manuscript.
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El Allaoui, A., Melliani, S., Chadli, L.S. (2020). Fuzzy Solutions for Impulsive Evolution Equations. In: Zerrik, E., Melliani, S., Castillo, O. (eds) Recent Advances in Modeling, Analysis and Systems Control: Theoretical Aspects and Applications. Studies in Systems, Decision and Control, vol 243. Springer, Cham. https://doi.org/10.1007/978-3-030-26149-8_5
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