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Sobolev Type Fractional Dynamic Equations and Optimal Multi-Integral Controls with Fractional Nonlocal Conditions
- Source :
- Fractional Calculus and Applied Analysis; February 2015, Vol. 18 Issue: 1 p95-121, 27p
- Publication Year :
- 2015
-
Abstract
- In 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.
Details
- Language :
- English
- ISSN :
- 13110454 and 13142224
- Volume :
- 18
- Issue :
- 1
- Database :
- Supplemental Index
- Journal :
- Fractional Calculus and Applied Analysis
- Publication Type :
- Periodical
- Accession number :
- ejs35052835
- Full Text :
- https://doi.org/10.1515/fca-2015-0007