Sobolev Type Fractional Dynamic Equations and Optimal Multi-Integral Controls with Fractional Nonlocal Conditions

Abstract

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.

This is a preprint of a paper whose final and definite form will appear in Fract. Calc. Appl. Anal. Paper submitted 10/April/2014; accepted for publication 21/Sept/2014

References in corpus (2)

• Modified Optimal Energy and Initial Memory of Fractional Continuous-Time Linear Systems
• Existence and Uniqueness of Solution to a Functional Integro-differential Fractional Equation