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We propose and investigate an evolution system with a RiemannLiouville fractional derivative. With the aid of a resolvent method, we formulate a suitable notion of solutions to this system and demonstrate the corresponding existence and uniqueness of solutions under a regular integral contractor condition. Furthermore, by applying a space decomposition technique, we exhibit the approximate controllability result of the system. This paper closes with a simple example, which confirms our analytical findings.

APPROXIMATE CONTROLLABILITY OF RIEMANN-LIOUVILLE FRACTIONAL EVOLUTION EQUATIONS WITH INTEGRAL CONTRACTOR ASSUMPTION