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Some new existence results for fractional differential inclusions with boundary conditions. (English) Zbl 1165.34313
Summary: This paper is mainly concerned with the existence of solutions for a certain class of fractional differential inclusions with boundary conditions. By using Bohnenblust-Karlin’s fixed point theorem, a main existence theorem is obtained. As an application of this main theorem, we establish two existence results when the multi-valued nonlinearity $F$ has sub-linear or linear growth in the state variable $y$. Our results are even new when applied to a corresponding single-valued problem.

34A60Differential inclusions
26A33Fractional derivatives and integrals (real functions)
34B15Nonlinear boundary value problems for ODE
Full Text: DOI
[1] Abbasbandy, S.; Nieto, J. J.; Alavi, M.: Tuning of reachable set in one dimensional fuzzy differential inclusions, Chaos solitons fractals 26, 1337-1341 (2005) · Zbl 1073.65054 · doi:10.1016/j.chaos.2005.03.018
[2] Benchohra, M.; Henderson, J.; Ntouyas, S. K.: On nonresonance second order impulsive functional differential inclusions with nonlinear boundary conditions, Can. appl. Math. Q. 14, 21-32 (2006) · Zbl 1146.34055
[3] M. Benchohra, J. Henderson, S.K. Ntouyas, A. Ouahab, Existence results for fractional order functional differential equations with infinite delay, J. Math. Anal. Appl. (in press) · Zbl 1209.34096 · doi:10.1016/j.jmaa.2007.06.021
[4] Bohnenblust, H. F.; Karlin, S.: On a theorem of ville, Contributions to the theory of games, 155-160 (1950) · Zbl 0041.25701
[5] Chang, Y. K.; Li, W. T.: Existence results for second order impulsive functional differential inclusions, J. math. Anal. appl. 301, 477-490 (2005) · Zbl 1067.34083 · doi:10.1016/j.jmaa.2004.07.041
[6] Chang, Y. K.; Li, W. T.; Nieto, J. J.: Controllability of evolution differential inclusions in Banach spaces, Nonlinear anal. TMA 67, 623-632 (2007) · Zbl 1128.93005 · doi:10.1016/j.na.2006.06.018
[7] Delbosco, D.; Rodino, L.: Existence and uniqueness for a nonlinear fractional differential equations, J. math. Anal. appl. 204, 609-625 (1996) · Zbl 0881.34005 · doi:10.1006/jmaa.1996.0456
[8] Deimling, K.: Multivalued differential equations, (1992) · Zbl 0760.34002
[9] Frigon, M.: Systems of first order differential inclusions with maximal monotone terms, Nonlinear anal. TMA 66, 2064-2077 (2007) · Zbl 1121.34017 · doi:10.1016/j.na.2006.03.002
[10] Ei-Sayed, A. M. A.: On the fractional differential equations, Appl. math. Comput. 49, 205-213 (1992) · Zbl 0757.34005 · doi:10.1016/0096-3003(92)90024-U
[11] Ei-Sayed, A. M. A: Nonlinear functional differential equations of arbitrary order, Nonlinear anal. TMA 33, 181-186 (1998) · Zbl 0934.34055 · doi:10.1016/S0362-546X(97)00525-7
[12] Ei-Sayed, A. M. A; Ibrahim, A. -G.: Set-valued integral equations of fractional-orders, Appl. math. Comput. 118, 113-121 (2001) · Zbl 1024.45003 · doi:10.1016/S0096-3003(99)00087-9
[13] Hu, S.; Papageorgiou, N.: Handbook of multivalued analysis, (1997) · Zbl 0887.47001
[14] Ibrahin, R. W.; Momani, S.: On the existence and uniqueness of solutions of a class of fractional differential equations, J. math. Anal. appl. 334, 1-10 (2007) · Zbl 1123.34302 · doi:10.1016/j.jmaa.2006.12.036
[15] V. Lakshmikantham, Theory of fractional functional differential equations, Nonlinear Anal. TMA (in press) · Zbl 1162.34344 · doi:10.1016/j.na.2007.09.025
[16] V. Lakshmikantham, A.S. Vatsala, Basic theory of fractional differential equations, Nonlinear Anal. TMA (in press) · Zbl 1161.34001
[17] Lasota, A.; Opial, Z.: An application of the Kakutani-Ky Fan theorem in the theory of ordinary differential equations, Bull. acad. Pol sci., ser.sci. Math. astronom. Phys. 13, 781-786 (1965) · Zbl 0151.10703
[18] Smirnov, G. V.: Introduction to the theory of differential inclusions, (2002) · Zbl 0992.34001
[19] Sun, J. P.; Zhao, Y. H.: Multiplicity of positive solutions of a class of nonlinear fractional differential equations, Comput. math. Appl. 49, 73-80 (2005) · Zbl 1085.34501 · doi:10.1016/j.camwa.2005.01.006
[20] Yu, C.; Gao, G.: Existence of fractional differential equations, J. math. Anal. appl. 310, 26-29 (2005) · Zbl 1088.34501 · doi:10.1016/j.jmaa.2004.12.015
[21] Yu, C.; Gao, G.: On the solution of nonlinear fractional order differential equation, Nonlinear anal. TMA 63, e971-e976 (2005) · Zbl 1224.34005 · doi:10.1016/j.na.2005.01.008
[22] Zhang, S.: The existence of a positive solution for a nonlinear fractional differential equation, J. math. Anal. appl. 252, 804-812 (2000) · Zbl 0972.34004 · doi:10.1006/jmaa.2000.7123
[23] Zhang, S.: Existence of positive solution for some class of nonlinear fractional differential equations, J. math. Anal. appl. 278, 136-148 (2003) · Zbl 1026.34008 · doi:10.1016/S0022-247X(02)00583-8
[24] Zhang, S.: Existence of positive solutions for fractional differential equations with Riemann--Liouville left-sided and right-hand fractional derivatives, Electron. J. Differential equations2004, 1-12 (2004) · Zbl 1050.34003 · emis:journals/EJDE/Volumes/2004/23/abstr.html
[25] Zhang, S.: Existences of solutions for a boundary value problem of fractional order, Acta math. Sci. 26 B, 220-228 (2006) · Zbl 1106.34010 · doi:10.1016/S0252-9602(06)60044-1