Regularity for fractional order retarded neutral differential equations in Hilbert spaces
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In this paper, we study the existence of solutions and $L^2$-regularity for fractional order retarded neutral functional differential equations in Hilbert spaces. We no longer require the compactness of structural operators to prove the existence of continuous solutions of the nonlinear differential system, but instead we investigate the relation between the regularity of solutions of fractional order retarded neutral functional differential systems with unbounded principal operators and that of its corresponding linear system excluded by the nonlinear term. Finally, we give a simple example to which our main result can be applied.
Abstract
In this paper, we study the existence of solutions and $L^2$-regularity for fractional order retarded neutral functional differential equations in Hilbert spaces. We no longer require the compactness of structural operators to prove the existence of continuous solutions of the nonlinear differential system, but instead we investigate the relation between the regularity of solutions of fractional order retarded neutral functional differential systems with unbounded principal operators and that of its corresponding linear system excluded by the nonlinear term. Finally, we give a simple example to which our main result can be applied.
참고문헌 (26)
- J. P. Aubin, "Un th`eor´eme de compacit´e", C. R. Acad. Sci, 256, pp.5042~5044 (1963)
- B. Baeumer, "Inhomogeneous fractional diffusion equations", Fract. Calc. Appl. Anal, 8(4), pp.371~386 (2005)
- G. Di Blasio, "L 2-regularity for parabolic partial integrodifferential equations with delay in the highest-order derivatives", J. Math. Anal. Appl, 102(1), pp.38~57 (1984)
- X. Fu, "Controllability of neutral functional differential systems in abstract space", Appl. Math. Comput, 141(2-3), pp.281~296 (2003)
- L. Gaul, "Damping description involving fractional operators", Mech. Syst. Signal Process, 5, pp.81~88 (1991)
- W. G. Glockle, "A fractional calculus approach of self-similar protein dynamics", Biophys. J, 68, pp.46~53 (1995)
- E. Hern´andez, "On state-dependent delay partial neutral functional differential equations", Appl. Math. Comput, 186(1), pp.294~301 (2007)
- E. Hern´andez, "Existence results for partial neutral functional differential equations with state-dependent delay", Math. Comput. Modelling, 49(5-6), pp.1260~1267 (2009)
- R. Hilfer, "Applications of Fractional Calculus in Physics" (2000), World Scientific
- O. K. Jaradat, "Existence of the mild solution for fractional semilinear initial value problems", Nonlinear Anal, 69(9), pp.3153~3159 (2008)
- J. M. Jeong, "Stabilizability of retarded functional differential equation in Hilbert space", Osaka J. Math, 28(2), pp.347~365 (1991)
- Jin-Mun Jeong, "Controllability for semilinear functional integrodifferential equations", 대한수학회보, 46(3), pp.463~475 (2009), 대한수학회
- J. M. Jeong, "Approximate controllability for semilinear retarded functional differential equations", J. Dynam. Control Systems, 5(3), pp.329~346 (1999)
- A. A. Kilbas, "North-Holland Mathematics Studies, vol. 204" (2006), Elsevier Science B.V
- M. A. Krannoselski, "Topological Methods in the Theory of Nonlinear Integral Equations" (1964), Pergamon Press
- V. Lakshmikantham, "Theory of Fractional Dynamic Systems" (2009), Cambridge Scientific Publishers
- F. Mainardi, "Fractals and fractional calculus in continuum mechanics", pp.291~348 (1997), Springer
- K. S. Miller, "An Introduction to the Fractional Calculus and Differential Equations" (1993), John Wiley
- M. Muslim, "Existence and approximation of solutions to fractional differential equations", Math. Comput. Modelling, 49(5-6), pp.1164~1172 (2009)
- I. Podlubny, "Fractional Differential Equations" (1999), Academic Press
- N. Sukavanam, "Approximate controllability of fractional order semilinear delay systems", J. Optim. Theory Appl, 151(2), pp.373~384 (2011)
- N. Sukavanam, "Approximate controllability of semilinear delay control system", Nonlinear Funct. Anal. Appl, 12(1), pp.53~59 (2007)
- H. Tanabe, "Equations of Evolution" (1979), Pitman
- H. Triebel, "Interpolation Theory, Function Spaces" (1978), Differential Operators
- L. Wang, "Approximate controllability for integrodifferential equations and multiple delays", J. Optim. Theory Appl, 143(1), pp.185~206 (2009)
- Y. Zhou, "Existence of mild solutions for fractional neutral evolution equations", Comput. Math. Appl, 59(3), pp.1063~1077 (2010)