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Controllability results for fractional integrodifferential systems with boundary conditions. (English) Zbl 1473.34007

Summary: This paper focuses the sufficient conditions for controllability of fractional integrodifferential systems with boundary conditions in Banach spaces. The results are obtained by using fractional calculus and fixed point theorem.

MSC:

34A08 Fractional ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
93B05 Controllability
47H10 Fixed-point theorems
Full Text: DOI

References:

[1] Agarwal, RP; Benchohra, M.; Hamanani, S., A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions, Acta Appl. Math., 109, 973-1033 (2010) · Zbl 1198.26004 · doi:10.1007/s10440-008-9356-6
[2] Anguraj, A.; Karthikeyan, P.; N’Guerekata, GM, Nonlocal Cauchy problem for some fractional abstract integrodifferential equations in Banach space, Commun. Math. Anal., 6, 31-35 (2009) · Zbl 1167.34387
[3] Balachandran, K.; Dauer, JP, Controllability of nonlinear systems via fixed point theorems, Journal of Optimization Theory and Applications, 53, 345-352 (1987) · Zbl 0596.93010 · doi:10.1007/BF00938943
[4] Balachandran, K.; Dauer, JP, Controllability of nonlinear systems in Banach spaces: A survey, Journal of Optimization Theory and Applications, 115, 7-28 (2002) · Zbl 1023.93010 · doi:10.1023/A:1019668728098
[5] Balachandran, K.; Park, JY, Controllability of fractional integrodifferential systems in Banach spaces, Nonlinear Analysis: Hybrid Systems, 3, 363-367 (2009) · Zbl 1175.93028
[6] Bonilla, B.; Rivero, M.; Rodriguez-Germa, L.; Trujillo, JJ, Fractional differential equations as alternative models to nonlinear differential equations, Applied Mathematics and Computation, 187, 79-88 (2007) · Zbl 1120.34323 · doi:10.1016/j.amc.2006.08.105
[7] K. Diethelm and A. D. Freed, On the solution of nonlinear fractional-order differential equation used in the modeling of viscoplasticity. In: F.keil, W.Mackens, H.Voss, J. Werther (Eds), Scientific Computing in Chemical Engineering II- Computational Fluid Dynamics, Reaction Engineering and Molecular Properties, Springer-Verlag, Heidelberg (1999), 217-224.
[8] Karthikeyan, P., Some results for boundary value problem of an integrodifferential equations with fractional order, Dynamic Systems and Applications, 20, 17-24 (2011) · Zbl 1235.34180
[9] Karthikeyan, K.; Trujillo, JJ, Existence and uniqueness results for fractional integrodifferential equations with boundary value conditions, Communications in Nonlinear Science and Numerical Simulation, 17, 4037-4043 (2012) · Zbl 1248.35216 · doi:10.1016/j.cnsns.2011.11.036
[10] Kilbas, AA; Srivastava, HM; Trujillo, JJ, Theory and Applications of Fractional Differential equations (2006), Amsterdam: Elsevier, Amsterdam · Zbl 1092.45003
[11] Klamka, J., Controllability of Dynamical Systems (1991), Dordrecht: Kluwer Academic, Dordrecht · Zbl 0732.93008
[12] Lakshmikantham, V., Theory of fractional functional differential equations, Nonlinear Anal., 69, 3337-3343 (2008) · Zbl 1162.34344 · doi:10.1016/j.na.2007.09.025
[13] Lakshmikantham, V.; Vatsala, AS, Basic theory of fractional differential equation, Nonlinear Anal., 69, 2677-2682 (2008) · Zbl 1161.34001 · doi:10.1016/j.na.2007.08.042
[14] Li, T.; Pintus, N.; Viglialoro, G., Properties of solutions to porous medium problems with different sources and boundary conditions, Z. Angew. Math. Phys., 70, 86 (2019) · Zbl 1415.35156 · doi:10.1007/s00033-019-1130-2
[15] Li, T.; Viglialoro, G., Analysis and explicit solvability of degenerate tensorial problems, Bound. Value Probl., 2018, 2 (2018) · Zbl 1382.35077 · doi:10.1186/s13661-017-0920-8
[16] Lin, W., Global existence theory and chaos control of fractional differential equation, J. Math. Anal. Appl., 332, 709-726 (2007) · Zbl 1113.37016 · doi:10.1016/j.jmaa.2006.10.040
[17] Pazy, A., Semigroups of Linear operators and Applications to Partial Differential Equations (1983), New York: Springer-Verlag, New York · Zbl 0516.47023 · doi:10.1007/978-1-4612-5561-1
[18] Podlubny, I., Fractional Differential Equations (1999), San Diego: Academic Press, San Diego · Zbl 0924.34008
[19] Smart, DR, Fixed point Theorems (1980), Cambridge: Cambridge University Press, Cambridge · Zbl 0427.47036
[20] Samko, SG; Kilbas, AA; Marichev, OI, Fractional Integrals and derivatives (1993), Gordon and Breach, Yverdon: Theory and Applications, Gordon and Breach, Yverdon · Zbl 0818.26003
[21] Wang, P.; Wang, Y.; Jiang, C.; Li, T., Convergence of solutions for functional integrodifferential equations with nonlinear boundary conditions, Adv. Difference Equ., 2019, 521 (2019) · Zbl 1487.45009 · doi:10.1186/s13662-019-2456-y
[22] Zhang, S., Positive solutions for boundary value problems for nonlinear fractional differential equations, Elec. J. Diff. Eqn., 36, 1-12 (2006) · Zbl 1096.34016
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