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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:

34A08 Fractional ordinary differential equations
34A37 Ordinary differential equations with impulses
34G20 Nonlinear differential equations in abstract spaces
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[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
[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
[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
[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
[6] Agarwal, R. P.; Benchohra, M.; Hamani, S., Boundary value problems for differential inclusions with fractional order, Adv. Stud. Contemp. Math., 16, 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, 10, 1-11 (2009) · Zbl 1178.34004
[8] Benchohra, M.; Berhoun, F., Impulsive fractional differential equations with variable times, Comput. Math. Appl., 59, 1245-1252 (2010) · Zbl 1189.34007
[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
[10] Luchko, Y.; Gorenflo, R., An operational method for fractional differential equations with the Caputo derivatives, Acta Math. Vietnam., 24, 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.; 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), Birkhäuser: Birkhäuser Basel, Boston, Berlin · Zbl 0816.35001
[13] Kilbas, A. A.; Srivastava, H. M.; Trujillo, J. J., Theory and Applications of Fractional Differential Equations (2006), Elsevier · Zbl 1092.45003
[14] Gorenflo, R.; Mainardi, F., (Fractional Calculus: Integral and Differential Equations of Fractional Order. Fractional Calculus: Integral and Differential Equations of Fractional Order, CISM Courses and Lectures, vol. 378 (1997), Springer- Verlag: Springer- Verlag Berlin) · Zbl 1438.26010
[15] E. Bazhlekova, Fractional evolution equations in Banach spaces, Ph.D. Thesis, Eindhoven University of Technology, 2001.; E. Bazhlekova, Fractional evolution equations in Banach spaces, Ph.D. Thesis, Eindhoven University of Technology, 2001.
[16] Prüss, J., Evolutionary Intergral Equations and Applications (1993), Birkhäuser: Birkhäuser Basel, Boston, Berlin
[17] Granas, A.; Dugundji, J., Fixed Point Theory (2003), Springer-Verlag: Springer-Verlag New York · Zbl 1025.47002
[18] Martin, R. H., Nonlinear Operators and Differential Equations in Banach Spaces (1987), Robert E. Krieger Publ. Co.: Robert E. Krieger Publ. Co. Florida
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