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 (4)

• Fractional Calculus: Some Basic Problems in Continuum and Statistical Mechanics
• Modified Optimal Energy and Initial Memory of Fractional Continuous-Time Linear Systems
• Approximate Controllability of Fractional Nonlocal Delay Semilinear Systems in Hilbert Spaces
• Existence and Uniqueness of Solution to a Functional Integro-differential Fractional Equation

Cited by in corpus (5)

• A survey on fuzzy fractional differential and optimal control nonlocal evolution equations
• Existence and uniqueness results for a fractional Riemann-Liouville nonlocal thermistor problem on arbitrary time scales
• Enlarged Controllability of Riemann-Liouville Fractional Differential Equations
• Approximate Controllability of Impulsive Non-local Non-linear Fractional Dynamical Systems and Optimal Control
• Regional Enlarged Observability of Fractional Differential Equations with Riemann-Liouville Time Derivatives