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Zbl 1228.34093
Sakthivel, R.; Ren, Yong; Mahmudov, N.I.
On the approximate controllability of semilinear fractional differential systems. (English)
[J] Comput. Math. Appl. 62, No. 3, 1451-1459 (2011). ISSN 0898-1221

Summary: Fractional differential equations have wide applications in science and engineering. We consider a class of control systems governed by the semilinear fractional differential equations in Hilbert spaces. By using the semigroup theory, the fractional power theory and fixed point strategy, a new set of sufficient conditions are formulated which guarantees the approximate controllability of semilinear fractional differential systems. The results are established under the assumption that the associated linear system is approximately controllable. Further, we extend the result to study the approximate controllability of fractional systems with nonlocal conditions. An example is provided to illustrate the application of the obtained theory.

MSC 2000:: *34H05 ODE in connection with control problems
34A08
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces

Keywords: approximate controllability; fractional differential equations; compact operators; semigroup theory

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Zentralblatt MATH Berlin [Germany]