Controllability of nonlinear implicit fractional integrodifferential systems

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1. Anichini, G., Conti, G. and Zecca, P. (1986). A note on controllability of certain nonlinear system, Note di Mathematica 6(2): 99-111. Zbl0612.93008
2. Balachandran, K. (1988). Controllability of nonlinear systems with implicit derivatives, IMA Journal of Mathematical Control and Information 5(2): 77-83. Zbl0662.93006
3. 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. Zbl0596.93010
4. Balachandran, K. and Balasubramaniam, P. (1992). A note on controllability of nonlinear Volterra integrodifferential systems, Kybernetika 28(4): 284-291. Zbl0771.93007
5. Balachandran, K. and Balasubramaniam, P. (1994). Controllability of nonlinear neutral Volterra integrodifferential systems, Journal of the Australian Mathematical Society 36(1): 107-116. Zbl0820.93035
6. 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. Zbl1302.93042
7. Balachandran, K. and Kokila, J. (2013a). Constrained controllability of fractional dynamical systems, Numerical Functional Analysis and Optimization 34(11): 1187-1205. Zbl1279.93021
8. Balachandran, K. and Kokila, J. (2013b). Controllability of nonlinear implicit fractional dynamical systems, IMA Journal of Applied Mathematics 79(3): 562-570. Zbl1304.34005
9. 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. Zbl1268.93021
10. 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. Zbl1277.34006
11. 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. Zbl1248.93022
12. Burton, T.A. (1983). Volterra Integral and Differential Equations, Academic Press, New York, NY. Zbl0515.45001
13. 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. 
14. Dacka, C. (1980). On the controllability of a class of nonlinear systems, IEEE Transaction on Automatic Control 25(2): 263-266. Zbl0439.93006
15. Kaczorek, K. (2011). Selected Problems of Fractional Systems Theory, Springer, Berlin. Zbl1221.93002
16. Kexue, L. and Jigen, P. (2011). Laplace transform and fractional differential equations, Applied Mathematics Letters 24(12): 2019-2013. Zbl1238.34013
17. Kilbas, A.A., Srivastava, H.M. and Trujillo, J.J. (2006). Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam. Zbl1092.45003
18. Klamka, J. (1975a). On the global controllability of perturbed nonlinear systems, IEEE Transactions on Automatic Control AC-20(1): 170-172. Zbl0299.93007
19. Klamka, J. (1975b). On the local controllability of perturbed nonlinear systems, IEEE Transactions on Automatic Control AC-20(2): 289-291. Zbl0299.93006
20. Klamka, J. (1975c). Controllability of nonlinear systems with delays in control, IEEE Transactions on Automatic Control AC-20(5): 702-704. Zbl0319.93011
21. Klamka, J. (1993). Controllability of Dynamical Systems, Kluwer Academic, Dordrecht. Zbl0797.93004
22. Klamka, J. (1999). Constrained controllability of dynamic systems, International Journal of Applied Mathematics and Computer Science 9(2): 231-244. Zbl0959.93004
23. Klamka, J. (2000). Schauder's fixed-point theorem in nonlinear controllability problems, Control and Cybernetics 29(1): 153-165. Zbl1011.93001
24. Klamka, J. (2001). Constrained controllability of semilinear delayed systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 49(3): 505-515. Zbl0999.93009
25. Klamka, J. (2008). Constrained controllability of semilinear systems with delayed controls, Bulletin of the Polish Academy of Sciences: Technical Sciences 56(4): 333-337. 
26. 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. Zbl1222.93030
27. Miller, K.S. and Ross, B. (1993). An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York, NY. Zbl0789.26002
28. 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. 
29. Oldham, K.B and Spanier, J. (1974). The Fractional Calculus, Academic Press, London. Zbl0292.26011
30. Olmstead, W.E. and Handelsman, R.A. (1976). Diffusion in a semi-infinite region with nonlinear surface dissipation, SIAM Review 18(2): 275-291. Zbl0323.45008
31. Podlubny, I. (1999). Fractional Differential Equations, Academic Press, New York, NY. Zbl0924.34008
32. Rawashdeh, E.A. (2011). Legendre wavelets method for fractional integrodifferential equations, Applied Mathematical Sciences 5(2): 2467-2474. Zbl1250.65160
33. Sadovskii, J.B. (1972). Linear compact and condensing operator, Russian Mathematical Surveys 27(1): 85-155. 
34. 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. Zbl1116.00014
35. Samko, S.G., Kilbas, A.A. and Marichev, O.I. (1993). Fractional Integrals and Derivatives; Theory and Applications, Gordon and Breach, Amsterdam. Zbl0818.26003

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