Controllability of solutions for semilinear fractional integrodifferential equations in Banach spaces
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Abstract
The study aims to prove the controllability of mild solution for semilinar fractional integerodifferential equations with nonlocal conditions in banach spaces.
Fractional calculus, compact semigroups and fixed point theorem, are concepts consulted to obtain results this work.
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References
[1] Al – Omar A., Jaradat O.K., Momani S., "Existence of mild solutions for fractional semi linear initial value Problem", nonlinear, Analysis, 69 (2008) 3153 – 3159.
[2] El – Borai M. M., "Semi groups and some nonlinear fractional differential equations", Applied Mathematics and computation, 149 (2004) 823 – 831.
[3] Ross, B., M. K. S., "An introduction to the fractional calculus and differential equations", John Wiley, New York, 1993.
[4] Triggiani, R., L. I., "Exact controllability of semi linear abstract systems with application to waves and plates boundary control problems", Appl. Math. Optim., 23 (1991), 109 – 154.
[5] Lee H., A. S., "Mon linear nonlocal Cauchy problems in Banach spaces", applied Mathematics letters", 18 (2005) 401 – 407.
[6] Erwin K., "Introduction Functional Analysis with application", by John.
[7] Siddiq, A. H., "Functional Analysis with applications", McGral – Hill Publishing company limited, 1986.
[8] Agarwal R. P. Benchohra M., Slimani B. A., "Existence results for differential efuations with fractionl equations with fractional order and impulsive", 44 (2008), 1-21.
[9] Zhang, S., "Positive solutions for boundary – value problems of nonlinear fractional differential equations", Electron. J. Differential Equations. Vol. 20069 (2006), No. 36, PP. 1-12
[10] Zeidler, E., "Nonlinear Functional Analysis and Hs Applications II / A, B", Springer – Verlag, New York, Inc., 1990.