This work analyzes the existence of solution and approximate
controllability for higher order non-linear fractional
integro-differential systems with Riemann-Liouville derivatives in
Banach spaces. Firstly, the definition of mild solution for the system
is derived. Then a set of sufficient conditions for the existence of
mild solution and approximate controllability of the system is obtained.
The discussions are based on fixed point approach, and the theory of
convolution and fractional resolvent. To illustrate the feasibility of
developed theory, an example is given.