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Approximate controllability of impulsive Riemann-Liouville fractional equations in Banach spaces. (English) Zbl 1303.93041

Summary: In this paper, we study control systems governed by impulsive Riemann-Liouville fractional differential equations in Banach spaces. Firstly, we introduce \(PC_{1-\alpha}\)-mild solutions for impulsive Riemann-Liouville fractional differential equations. Then, we make a set of assumptions to guarantee the existence and uniqueness of mild solutions. Finally, approximate controllability of the associated impulsive Riemann-Liouville fractional evolution control systems is also formulated and proved.

MSC:

93B05 Controllability
34A08 Fractional ordinary differential equations
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