Acknowledgement
Supported by : National Foundation of Korea(NRF)
References
- J. P. Aubin, Un theoreme de compacite, C. R. Acad. Sci. 256 (1963), 5042-5044.
- B. Baeumer, S. Kurita, and M. M. Meerschaert, Inhomogeneous fractional diffusion equations, Fract. Calc. Appl. Anal. 8 (2005), no. 4, 371-386.
-
G. Di Blasio, K. Kunisch, and E. Sinestrari,
$L^2$ -regularity for parabolic partial integrod-ifferential equations with delay in the highest-order derivatives, J. Math. Anal. Appl. 102 (1984), no. 1, 38-57. https://doi.org/10.1016/0022-247X(84)90200-2 - X. Fu, Controllability of neutral functional differential systems in abstract space, Appl. Math. Comput. 141 (2003), no. 2-3, 281-296. https://doi.org/10.1016/S0096-3003(02)00253-9
- L. Gaul, P. Klein, and S. Kempfle, Damping description involving fractional operators, Mech. Syst. Signal Process. 5 (1991), 81-88. https://doi.org/10.1016/0888-3270(91)90016-X
- W. G. Glockle and T. F. Nonnenmacher, A fractional calculus approach of self-similar protein dynamics, Biophys. J. 68 (1995), 46-53. https://doi.org/10.1016/S0006-3495(95)80157-8
- E. Hernandez and M. Mckibben, On state-dependent delay partial neutral functional differential equations, Appl. Math. Comput. 186 (2007), no. 1, 294-301. https://doi.org/10.1016/j.amc.2006.07.103
- E. Hernandez, M. Mckibben, and H. Henrrquez, Existence results for partial neutral functional differential equations with state-dependent delay, Math. Comput. Modelling 49 (2009), no. 5-6, 1260-1267. https://doi.org/10.1016/j.mcm.2008.07.011
- R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000.
- O. K. Jaradat, A. Al-Omari, and S. Momani, Existence of the mild solution for fractional semilinear initial value problems, Nonlinear Anal. 69 (2008), no. 9, 3153-3159. https://doi.org/10.1016/j.na.2007.09.008
- J. M. Jeong, Stabilizability of retarded functional differential equation in Hilbert space, Osaka J. Math. 28 (1991), no. 2, 347-365.
- J. M. Jeong and H. G. Kim, Controllability for semilinear functional integrodifferential equations, Bull. Korean Math. Soc. 46 (2009), no. 3, 463-475. https://doi.org/10.4134/BKMS.2009.46.3.463
- J. M. Jeong, Y. C. Kwun, and J. Y. Park, Approximate controllability for semilinear retarded functional differential equations, J. Dynam. Control Systems 5 (1999), no. 3, 329-346. https://doi.org/10.1023/A:1021714500075
- A. A. Kilbas, H. M. Srivastava, and J. Juan Trujillo, Theory and Applications of Fractional Differential Equations, in: North-Holland Mathematics Studies, vol. 204, Elsevier Science B.V, Amsterdam, 2006.
- M. A. Krannoselski, Topological Methods in the Theory of Nonlinear Integral Equations, Pergamon Press, New York, 1964.
- V. Lakshmikantham, S. Leela, and J. V. Devi, Theory of Fractional Dynamic Systems, Cambridge Scientific Publishers, 2009.
- F. Mainardi, Fractional calculus: Some basic problems in continuum and statistical mechanics, Fractals and fractional calculus in continuum mechanics (Udine, 1996), 291-348, CISM Courses and Lectures, 378, Springer, Vienna, 1997.
- K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Differential Equations, John Wiley, New York, 1993.
- M.Muslim, Existence and approximation of solutions to fractional differential equations, Math. Comput. Modelling 49 (2009), no. 5-6, 1164-1172. https://doi.org/10.1016/j.mcm.2008.07.013
- I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
- N. Sukavanam and S. Kumar, Approximate controllability of fractional order semilinear delay systems, J. Optim. Theory Appl. 151 (2011), no. 2, 373-384. https://doi.org/10.1007/s10957-011-9905-4
- N. Sukavanam and N. K. Tomar, Approximate controllability of semilinear delay control system, Nonlinear Funct. Anal. Appl. 12 (2007), no. 1, 53-59.
- H. Tanabe, Equations of Evolution, Pitman-London, 1979.
- H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, 1978.
- L. Wang, Approximate controllability for integrodifferential equations and multiple delays, J. Optim. Theory Appl. 143 (2009), no. 1, 185-206. https://doi.org/10.1007/s10957-009-9545-0
- Y. Zhou and F. Jiao, Existence of mild solutions for fractional neutral evolution equations, Comput. Math. Appl. 59 (2010), no. 3, 1063-1077. https://doi.org/10.1016/j.camwa.2009.06.026