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Some existence results for impulsive nonlinear fractional differential equations with mixed boundary conditions. (English) Zbl 1228.34021
Summary: We investigate the existence and uniqueness of solutions for an impulsive mixed boundary value problem of nonlinear differential equations of fractional order α(1,2]. Our results are based on some standard fixed point theorems. Some examples are presented to illustrate the main results.
MSC:
34A08Fractional differential equations
34B37Boundary value problems for ODE with impulses
47H10Fixed point theorems for nonlinear operators on topological linear spaces
References:
[1]Samko, S. G.; Kilbas, A. A.; Marichev, O. I.: Fractional integrals and derivatives, theory and applications, (1993) · Zbl 0818.26003
[2]Podlubny, I.: Fractional differential equations, (1999)
[3]Kilbas, A. A.; Srivastava, H. M.; Trujillo, J. J.: Theory and applications of fractional differential equations, North-holland mathematics studies 204 (2006)
[4], Advances in fractional calculus: theoretical developments and applications in physics and engineering (2007)
[5]Lakshmikantham, V.; Leela, S.; Devi, J. Vasundhara: Theory of fractional dynamic systems, (2009)
[6]Lazarević, M. P.; Spasić, A. M.: Finite-time stability analysis of fractional order time-delay systems: Gronwall’s approach, Math. comput. Modelling 49, 475-481 (2009) · Zbl 1165.34408 · doi:10.1016/j.mcm.2008.09.011
[7]Agarwal, R. P.; Zhou, Y.; He, Y.: Existence of fractional neutral functional differential equations, Comput. math. Appl. 59, 1095-1100 (2010) · Zbl 1189.34152 · doi:10.1016/j.camwa.2009.05.010
[8]Zhou, Y.; Jiao, F.; Li, J.: Existence and uniqueness for fractional neutral differential equations with infinite delay, Nonlinear anal. 71, 3249-3256 (2009) · Zbl 1177.34084 · doi:10.1016/j.na.2009.01.202
[9]Zhou, Y.; Jiao, F.: Nonlocal Cauchy problem for fractional evolution equations, Nonlinear anal.: RWA 11, 4465-4475 (2010)
[10]Wang, J.; Zhou, Y.: A class of fractional evolution equations and optimal controls, Nonlinear anal.: RWA 12, 262-272 (2011) · Zbl 1214.34010 · doi:10.1016/j.nonrwa.2010.06.013
[11]Bai, Z. B.: On positive solutions of a nonlocal fractional boundary value problem, Nonlinear anal. 72, 916-924 (2010) · Zbl 1187.34026 · doi:10.1016/j.na.2009.07.033
[12]Ahmad, B.; Nieto, J. J.: Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions, Comput. math. Appl. 58, 1838-1843 (2009) · Zbl 1205.34003 · doi:10.1016/j.camwa.2009.07.091
[13]Ahmad, B.; Sivasundaram, S.: On four-point nonlocal boundary value problems of nonlinear integro-differential equations of fractional order, Appl. math. Comput. 217, 480-487 (2010) · Zbl 1207.45014 · doi:10.1016/j.amc.2010.05.080
[14]Wei, Z.; Li, Q.; Che, J.: Initial value problems for fractional differential equations involving Riemann-iouville sequential fractional derivative, J. math. Anal. appl. 367, 260-272 (2010) · Zbl 1191.34008 · doi:10.1016/j.jmaa.2010.01.023
[15]Ahmad, B.: Existence of solutions for fractional differential equations of order q(2,3] with anti-periodic boundary conditions, J. appl. Math. comput. 34, 385-391 (2010) · Zbl 1216.34003 · doi:10.1007/s12190-009-0328-4
[16]Nieto, J. J.: Maximum principles for fractional differential equations derived from Mittag–Leffler functions, Appl. math. Lett. 23, 1248-1251 (2010) · Zbl 1202.34019 · doi:10.1016/j.aml.2010.06.007
[17]Zhang, S. Q.: Positive solutions to singular boundary value problem for nonlinear fractional differential equation, Comput. math. Appl. 59, 1300-1309 (2010) · Zbl 1189.34050 · doi:10.1016/j.camwa.2009.06.034
[18]Ahmad, B.; Alsaedi, A.: Existence and uniqueness of solutions for coupled systems of higher order nonlinear fractional differential equations, Fixed point theory appl 2010, 17 (2010) · Zbl 1208.34001 · doi:10.1155/2010/364560
[19]G. Wang, L. Zhang, S.K. Ntouyas, Multiplicity of positive solutions for fractional-order three-point boundary value problems, Commun. Appl. Nonlinear Anal. (in press).
[20]Lakshmikantham, V.; Bainov, D. D.; Simeonov, P. S.: Theory of impulsive differential equations, (1989) · Zbl 0718.34011
[21]Samoilenko, A. M.; Perestyuk, N. A.: Impulsive differential equations, (1995) · Zbl 0837.34003
[22]Zavalishchin, S. T.; Sesekin, A. N.: Dynamic impulse systems. Theory and applications, (1997)
[23]Wang, G.; Zhang, L.; Song, G.: Extremal solutions for the first order impulsive functional differential equations with upper and lower solutions in reversed order, J. comput. Appl. math. 235, 325-333 (2010) · Zbl 1210.34110 · doi:10.1016/j.cam.2010.06.014
[24]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
[25]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
[26]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
[27]Chang, Y. -K.; Nieto, J. J.; Zhao, Zhi-Han: Existence results for a nondensely-defined impulsive neutral differential equation with state-dependent delay, Nonlinear anal.: hybrid syst. 4, 593-599 (2010) · Zbl 1209.34093 · doi:10.1016/j.nahs.2010.03.006
[28]Zhang, X.; Huang, X.; Liu, Z.: The existence and uniqueness of mild solutions for impulsive fractional equations with nonlocal conditions and infinite delay, Nonlinear anal. Hybrid syst. 4, 775-781 (2010) · Zbl 1207.34101 · doi:10.1016/j.nahs.2010.05.007
[29]Tian, Y.; Bai, Z.: Existence results for the three-point impulsive boundary value problem involving fractional differential equations, Comput. math. Appl. 59, 2601-2609 (2010) · Zbl 1193.34007 · doi:10.1016/j.camwa.2010.01.028
[30]R.P. Agarwal, B. Ahmad, Existence of solutions for impulsive anti-periodic boundary value problems of fractional semilinear evolution equations, Dyn. Contin. Discrete Impuls. Syst., Ser. A, Math. Anal. (in press). · Zbl 1226.26005 · doi:http://online.watsci.org/abstract_pdf/2011v18/v18n4a-pdf/3.pdf
[31]Wang, G.; Ahmad, B.; Zhang, L.: Impulsive anti-periodic boundary value problem for nonlinear differential equations of fractional order, Nonlinear anal. 74, 792-804 (2011) · Zbl 1214.34009 · doi:10.1016/j.na.2010.09.030
[32]Jahanshahi, M.: Reduction of the Neumann, Poincarè and Robin–zaremba boundary value problems for Laplace equation to the Dirichlet boundary value problem, Appl. comput. Math. 6, 51-57 (2007) · Zbl 1209.35036 · doi:http://www.science.az/acm/v_6_n_1_2007/titul.htm
[33]Den Berg, M. Van; Gilkey, P.; Kirsten, K.; Kozlov, V. A.: Heat content asymptotics for Riemannian manifolds with zaremba boundary conditions, Potential anal. 26, 225-254 (2007) · Zbl 1114.58022 · doi:10.1007/s11118-005-9001-1
[34]Avramidi, I. G.: Heat kernel asymptotics of zaremba boundary value problem, Math. phys. Anal. geom. 7, 9-46 (2004) · Zbl 1079.58018 · doi:10.1023/B:MPAG.0000022837.63824.4c
[35]Sun, J. X.: Nonlinear functional analysis and its application, (2008)