Controllability of nonlinear implicit fractional integrodifferential systems

Anichini, G., Conti, G. and Zecca, P. (1986). A note on controllability of certain nonlinear system, Note di Mathematica 6(2): 99-111.Search in Google Scholar

Balachandran, K. (1988). Controllability of nonlinear systems with implicit derivatives, IMA Journal of Mathematical Control and Information 5(2): 77-83.10.1093/imamci/5.2.77Search in Google Scholar

Balachandran, K. and Dauer, J.P. (1987). Controllability of nonlinear systems via fixed point theorems, Journal of Optimization Theory and Applications 53(3): 345-352.10.1007/BF00938943Search in Google Scholar

Balachandran, K. and Balasubramaniam, P. (1992). A note on controllability of nonlinear Volterra integrodifferential systems, Kybernetika 28(4): 284-291.Search in Google Scholar

Balachandran, K. and Balasubramaniam, P. (1994).Search in Google Scholar

Controllability of nonlinear neutral Volterra integrodifferential systems, Journal of the Australian Mathematical Society 36(1): 107-116.10.1017/S0334270000010274Search in Google Scholar

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/v10006-012-0039-0.10.2478/v10006-012-0039-0Search in Google Scholar

Balachandran, K. and Kokila, J. (2013a). Constrained controllability of fractional dynamical systems, Numerical Functional Analysis and Optimization 34(11): 1187-1205.10.1080/01630563.2013.778868Search in Google Scholar

Balachandran, K. and Kokila, J. (2013b). Controllability of nonlinear implicit fractional dynamical systems, IMA Journal of Applied Mathematics 79(3): 562-570.10.1093/imamat/hxt003Search in Google Scholar

Balachandran, K., Kokila, J. and Trujillo, J.J. (2012b).Search in Google Scholar

Relative controllability of fractional dynamical systems with multiple delays in control, Computers and Mathematics with Applications 64(10): 3037-3045.10.1016/j.camwa.2012.01.071Search in Google Scholar

Balachandran, K., Park, J.Y. and Trujillo, J.J. (2012c).Search in Google Scholar

Controllability of nonlinear fractional dynamical systems, Nonlinear Analysis: Theory, Methods and Applications 75(4): 1919-1926.10.1016/j.na.2011.09.042Search in Google Scholar

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): 3508-3520.10.1016/j.cnsns.2011.12.018Search in Google Scholar

Burton, T.A. (1983). Volterra Integral and Differential Equations, Academic Press, New York, NY.Search in Google Scholar

Caputo, M. (1967). Linear model of dissipation whose Q is almost frequency independent, Part II, Geophysical Journal of Royal Astronomical Society 13(5): 529-539.10.1111/j.1365-246X.1967.tb02303.xSearch in Google Scholar

Dacka, C. (1980). On the controllability of a class of nonlinear systems, IEEE Transaction on Automatic Control 25(2): 263-266.10.1109/TAC.1980.1102287Search in Google Scholar

Kaczorek, K. (2011). Selected Problems of Fractional Systems Theory, Springer, Berlin.10.1007/978-3-642-20502-6Search in Google Scholar

Kexue, L. and Jigen, P. (2011). Laplace transform and fractional differential equations, Applied Mathematics Letters 24(12): 2019-2013.10.1016/j.aml.2011.05.035Search in Google Scholar

Kilbas, A.A., Srivastava, H.M. and Trujillo, J.J. (2006). Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam.Search in Google Scholar

Klamka, J. (1975a). On the global controllability of perturbed nonlinear systems, IEEE Transactions on Automatic Control AC-20(1): 170-172.10.1109/TAC.1975.1100870Search in Google Scholar

Klamka, J. (1975b). On the local controllability of perturbed nonlinear systems, IEEE Transactions on Automatic Control AC-20(2): 289-291.10.1109/TAC.1975.1100929Search in Google Scholar

Klamka, J. (1975c). Controllability of nonlinear systems with delays in control, IEEE Transactions on Automatic Control AC-20(5): 702-704.10.1109/TAC.1975.1101046Search in Google Scholar

Klamka, J. (1993). Controllability of Dynamical Systems, Kluwer Academic, Dordrecht.Search in Google Scholar

Klamka, J. (1999). Constrained controllability of dynamic systems, International Journal of Applied Mathematics and Computer Science 9(2): 231-244.Search in Google Scholar

Klamka, J. (2000). Schauder’s fixed-point theorem in nonlinear controllability problems, Control and Cybernetics 29(1): 153-165.Search in Google Scholar

Klamka, J. (2001). Constrained controllability of semilinear delayed systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 49(3): 505-515.Search in Google Scholar

Klamka, J. (2008). Constrained controllability of semilinear systems with delayed controls, Bulletin of the Polish Academy of Sciences: Technical Sciences 56(4): 333-337.Search in Google Scholar

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. 503-509.10.1007/978-90-481-3293-5_45Search in Google Scholar

Miller, K.S. and Ross, B. (1993). An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York, NY.Search in Google Scholar

Mittal, R.C. and Nigam, R. (2008). Solution of fractional integrodifferential equations by Adomian decomposition method, International Journal of AppliedMathematics and Mechanics 4(2): 87-94.Search in Google Scholar

Oldham, K.B and Spanier, J. (1974). The Fractional Calculus, Academic Press, London.Search in Google Scholar

Olmstead, W.E. and Handelsman, R.A. (1976). Diffusion in a semi-infinite region with nonlinear surface dissipation, SIAM Review 18(2): 275-291.10.1137/1018044Search in Google Scholar

Podlubny, I. (1999). Fractional Differential Equations, Academic Press, New York, NY. Search in Google Scholar