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The existence of mild solutions for impulsive fractional partial differential equations. (English) Zbl 1227.34009
The existence of mild solutions for a class of impulsive fractional partial semilinear differential equations is presented. The results generalize some known results.
MSC:
34A08Fractional differential equations
34A37Differential equations with impulses
34G20Nonlinear ODE in abstract spaces
References:
[1]Agarwal, R. P.; Benchohra, M.; Slimani, B. A.: Existence results for differential equations with fractional order and impulses, Mem. differential equations math. Phys. 44, 1-21 (2008) · Zbl 1178.26006
[2]Mophou, G. M.: Existence and uniqueness of mild solutions to impulsive fractional differential equations, Nonlinear anal. 72, 1604-1615 (2010) · Zbl 1187.34108 · doi:10.1016/j.na.2009.08.046
[3]Tai, Z.; Wang, X.: Controllability of fractional-order impulsive neutral functional infinite delay integrodifferential systems in Banach spaces, Appl. math. Lett. 22, 1760-1765 (2009) · Zbl 1181.34078 · doi:10.1016/j.aml.2009.06.017
[4]Ahmad, B.; Sivasundaram, S.: Existence of solutions for impulsive integral boundary value problems of fractional order, Nonlinear anal. Hybrid syst. 4, 134-141 (2010) · Zbl 1187.34038 · doi:10.1016/j.nahs.2009.09.002
[5]Ahmad, B.; Sivasundaram, S.: Existence results for nonlinear impulsive hybrid boundary value problems involving fractional differential equations, Nonlinear anal. Hybrid syst. 3, 251-258 (2009) · Zbl 1193.34056 · doi:10.1016/j.nahs.2009.01.008
[6]Agarwal, R. P.; Benchohra, M.; Hamani, S.: Boundary value problems for differential inclusions with fractional order, Adv. stud. Contemp. math. 16, No. 2, 181-196 (2008) · Zbl 1152.26005
[7]Benchohra, M.; Slimani, B. A.: Existence and uniqueness of solutions to impulsive fractional differential equations, Electron. J. Differential equations 2009, No. 10, 1-11 (2009) · Zbl 1178.34004 · doi:emis:journals/EJDE/Volumes/2009/10/abstr.html
[8]Benchohra, M.; Berhoun, F.: Impulsive fractional differential equations with variable times, Comput. math. Appl. 59, 1245-1252 (2010) · Zbl 1189.34007 · doi:10.1016/j.camwa.2009.05.016
[9]Mainardi, F.; Gorenflo, R.: On Mittag-Leffler-type functions in fractional evolution processes, J. comput. Appl. math. 118, 283-299 (2000) · Zbl 0970.45005 · doi:10.1016/S0377-0427(00)00294-6
[10]Luchko, Y.; Gorenflo, R.: An operational method for fractional differential equations with the Caputo derivatives, Acta math. Vietnam 24, No. 2, 207-233 (1999) · Zbl 0931.44003
[11]R. Gorenflo, F. Mainardi, Fractional oscillations and Mittag-Leffler functions, in: University Kuwait D.M.C.S. (Ed.) International Workshop on the Recent Advances in Applied Mathematics, Kuwait, Raam’96, Kuwait, 1996, pp. 193–208. · Zbl 0916.34011
[12]Lunardi, A.: Analytic semigroups and optimal regularity in parabolic problem, (1995)
[13]Kilbas, A. A.; Srivastava, H. M.; Trujillo, J. J.: Theory and applications of fractional differential equations, (2006)
[14]Gorenflo, R.; Mainardi, F.: Fractional calculus: integral and differential equations of fractional order, CISM courses and lectures 378 (1997)
[15]E. Bazhlekova, Fractional evolution equations in Banach spaces, Ph.D. Thesis, Eindhoven University of Technology, 2001. · Zbl 0989.34002
[16]Prüss, J.: Evolutionary intergral equations and applications, (1993)
[17]Granas, A.; Dugundji, J.: Fixed point theory, (2003)
[18]Martin, R. H.: Nonlinear operators and differential equations in Banach spaces, (1987) · Zbl 0649.47039