  We prove existence and uniqueness of mild solutions to Sobolev type
fractional nonlocal dynamic equations in Banach spaces. The Sobolev nonlocal
condition is considered in terms of a Riemann-Liouville fractional derivative.
A Lagrange optimal control problem is considered, and existence of a
multi-integral solution obtained. Main tools include fractional calculus,
semigroup theory, fractional power of operators, a singular version of
Gronwall's inequality, and Leray-Schauder fixed point theorem. An example
illustrating the theory is given.
