Electron. J. Diff. Equ., Vol. 2015 (2015), No. 89, pp. 1-18.

Relaxation in controlled systems described by fractional integro-differential equations with nonlocal control conditions

Amar Debbouche, Juan J. Nieto

A control system described by fractional evolution integro-differential equations and fractional integral nonlocal control conditions is investigated. This posed system is subjected to mixed multivalued control constraints whose values are nonconvex closed sets. Along with the original system, we consider the system in which the constraints on the controls are the closed convex hulls of the original constraints. More precisely, existence results for the mentioned nonlocal control systems are proved. Furthermore, we study relations between the solution sets of both two systems.

Submitted September 16, 2014. Published April 10, 2015.
Math Subject Classifications: 26A33, 45J05, 34G20, 93C23.
Key Words: Fractional integro-differential equation; relaxation property; feedback control; nonconvex constraint; nonlocal control condition.

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Amar Debbouche
Department of Mathematics
Guelma University
Guelma 24000, Algeria
email: amar_debbouche@yahoo.fr, amar.debbouche@usc.es
Juan J. Nieto
Departamento de Análisis Matemático
Universidad de Santiago de Compostela
Santiago de Compostela 15782, Spain
email: juanjose.nieto.roig@usc.es

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