Controllability of nonlinear implicit fractional integrodifferential systems
Krishnan Balachandran ; Shanmugam Divya
International Journal of Applied Mathematics and Computer Science, Tome 24 (2014), p. 713-722 / Harvested from The Polish Digital Mathematics Library

In this paper, we study the controllability of nonlinear fractional integrodifferential systems with implicit fractional derivative. Sufficient conditions for controllability results are obtained through the notion of the measure of noncompactness of a set and Darbo's fixed point theorem. Examples are included to verify the result.

Publié le : 2014-01-01
EUDML-ID : urn:eudml:doc:271902
@article{bwmeta1.element.bwnjournal-article-amcv24i4p713bwm,
     author = {Krishnan Balachandran and Shanmugam Divya},
     title = {Controllability of nonlinear implicit fractional integrodifferential systems},
     journal = {International Journal of Applied Mathematics and Computer Science},
     volume = {24},
     year = {2014},
     pages = {713-722},
     zbl = {1309.93025},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv24i4p713bwm}
}
Krishnan Balachandran; Shanmugam Divya. Controllability of nonlinear implicit fractional integrodifferential systems. International Journal of Applied Mathematics and Computer Science, Tome 24 (2014) pp. 713-722. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv24i4p713bwm/

[000] Anichini, G., Conti, G. and Zecca, P. (1986). A note on controllability of certain nonlinear system, Note di Mathematica 6(2): 99-111. | Zbl 0612.93008

[001] Balachandran, K. (1988). Controllability of nonlinear systems with implicit derivatives, IMA Journal of Mathematical Control and Information 5(2): 77-83. | Zbl 0662.93006

[002] Balachandran, K. and Dauer, J.P. (1987). Controllability of nonlinear systems via fixed point theorems, Journal of Optimization Theory and Applications 53(3): 345-352. | Zbl 0596.93010

[003] Balachandran, K. and Balasubramaniam, P. (1992). A note on controllability of nonlinear Volterra integrodifferential systems, Kybernetika 28(4): 284-291. | Zbl 0771.93007

[004] Balachandran, K. and Balasubramaniam, P. (1994). Controllability of nonlinear neutral Volterra integrodifferential systems, Journal of the Australian Mathematical Society 36(1): 107-116. | Zbl 0820.93035

[005] Balachandran, K. and Kokila, J. (2012a). On the controllability of fractional dynamical systems, International Journal of Applied Mathematics and Computer Science 22(3): 523-531, DOI: 10.2478/v10006-012-0039-0. | Zbl 1302.93042

[006] Balachandran, K. and Kokila, J. (2013a). Constrained controllability of fractional dynamical systems, Numerical Functional Analysis and Optimization 34(11): 1187-1205. | Zbl 1279.93021

[007] Balachandran, K. and Kokila, J. (2013b). Controllability of nonlinear implicit fractional dynamical systems, IMA Journal of Applied Mathematics 79(3): 562-570. | Zbl 1304.34005

[008] Balachandran, K., Kokila, J. and Trujillo, J.J. (2012b). Relative controllability of fractional dynamical systems with multiple delays in control, Computers and Mathematics with Applications 64(10): 3037-3045. | Zbl 1268.93021

[009] Balachandran, K., Park, J.Y. and Trujillo, J.J. (2012c). Controllability of nonlinear fractional dynamical systems, Nonlinear Analysis: Theory, Methods and Applications 75(4): 1919-1926. | Zbl 1277.34006

[010] Balachandran, K., Zhou, Y. and J. Kokila, J. (2012d). Relative controllability of fractional dynamical systems with delays in control, Communications in Nonlinear Science and Numerical Simulation 17(9): 3508-3520. | Zbl 1248.93022

[011] Burton, T.A. (1983). Volterra Integral and Differential Equations, Academic Press, New York, NY. | Zbl 0515.45001

[012] Caputo, M. (1967). Linear model of dissipation whose Q is almost frequency independent, Part II, Geophysical Journal of Royal Astronomical Society 13(5): 529-539.

[013] Dacka, C. (1980). On the controllability of a class of nonlinear systems, IEEE Transaction on Automatic Control 25(2): 263-266. | Zbl 0439.93006

[014] Kaczorek, K. (2011). Selected Problems of Fractional Systems Theory, Springer, Berlin. | Zbl 1221.93002

[015] Kexue, L. and Jigen, P. (2011). Laplace transform and fractional differential equations, Applied Mathematics Letters 24(12): 2019-2013. | Zbl 1238.34013

[016] Kilbas, A.A., Srivastava, H.M. and Trujillo, J.J. (2006). Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam. | Zbl 1092.45003

[017] Klamka, J. (1975a). On the global controllability of perturbed nonlinear systems, IEEE Transactions on Automatic Control AC-20(1): 170-172. | Zbl 0299.93007

[018] Klamka, J. (1975b). On the local controllability of perturbed nonlinear systems, IEEE Transactions on Automatic Control AC-20(2): 289-291. | Zbl 0299.93006

[019] Klamka, J. (1975c). Controllability of nonlinear systems with delays in control, IEEE Transactions on Automatic Control AC-20(5): 702-704. | Zbl 0319.93011

[020] Klamka, J. (1993). Controllability of Dynamical Systems, Kluwer Academic, Dordrecht. | Zbl 0797.93004

[021] Klamka, J. (1999). Constrained controllability of dynamic systems, International Journal of Applied Mathematics and Computer Science 9(2): 231-244. | Zbl 0959.93004

[022] Klamka, J. (2000). Schauder's fixed-point theorem in nonlinear controllability problems, Control and Cybernetics 29(1): 153-165. | Zbl 1011.93001

[023] Klamka, J. (2001). Constrained controllability of semilinear delayed systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 49(3): 505-515. | Zbl 0999.93009

[024] Klamka, J. (2008). Constrained controllability of semilinear systems with delayed controls, Bulletin of the Polish Academy of Sciences: Technical Sciences 56(4): 333-337.

[025] Klamka, J. (2010). Controllability and minimum energy control problem of fractional discrete time systems, in D. Baleanu, Z.B. Guvenc, and J.A.T. Machado (Eds.), New Trends in Nanotechnology and Fractional Calculus, Springer-Verlag, New York, NY, pp. 503-509. | Zbl 1222.93030

[026] Miller, K.S. and Ross, B. (1993). An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York, NY. | Zbl 0789.26002

[027] Mittal, R.C. and Nigam, R. (2008). Solution of fractional integrodifferential equations by Adomian decomposition method, International Journal of Applied Mathematics and Mechanics 4(2): 87-94.

[028] Oldham, K.B and Spanier, J. (1974). The Fractional Calculus, Academic Press, London. | Zbl 0292.26011

[029] Olmstead, W.E. and Handelsman, R.A. (1976). Diffusion in a semi-infinite region with nonlinear surface dissipation, SIAM Review 18(2): 275-291. | Zbl 0323.45008

[030] Podlubny, I. (1999). Fractional Differential Equations, Academic Press, New York, NY. | Zbl 0924.34008

[031] Rawashdeh, E.A. (2011). Legendre wavelets method for fractional integrodifferential equations, Applied Mathematical Sciences 5(2): 2467-2474. | Zbl 1250.65160

[032] Sadovskii, J.B. (1972). Linear compact and condensing operator, Russian Mathematical Surveys 27(1): 85-155.

[033] Sabatier, J., Agarwal, O.P. and Tenreiro Machado, J.A. (Eds.) (2007). Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering, Springer-Verlag, New York, NY. | Zbl 1116.00014

[034] Samko, S.G., Kilbas, A.A. and Marichev, O.I. (1993). Fractional Integrals and Derivatives; Theory and Applications, Gordon and Breach, Amsterdam. | Zbl 0818.26003