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Title: Sobolev type fractional dynamic equations and Optimal multi-integral controls with fractional nonlocal conditions
Author: Debbouche, Amar
Torres, Delfim F. M.
Keywords: Sobolev type equations
Fractional evolution equations
Optimal control
Nonlocal conditions
Mild solutions
Issue Date: Feb-2015
Publisher: Springer Verlag
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.
Peer review: yes
DOI: 10.1515/fca-2015-0007
ISSN: 1311-0454
Appears in Collections:CIDMA - Artigos

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