Geodesic
Relaxation in controlled systems described by fractional integro-differential equations with nonlocal control conditions
Electronic Journal of Differential Equations, Tome 2015 (2015).

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Summary: 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.
Classification : 26A33, 45J05, 34G20, 93C23
Keywords: fractional integro-differential equation, relaxation property, feedback control, nonconvex constraint, nonlocal control condition 
@article{EJDE_2015__2015__a47,
     author = {Debbouche, Amar and Nieto, Juan J.},
     title = {Relaxation in controlled systems described by fractional integro-differential equations with nonlocal control conditions},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2015},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a47/}
}
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Debbouche, Amar; Nieto, Juan J. Relaxation in controlled systems described by fractional integro-differential equations with nonlocal control conditions. Electronic Journal of Differential Equations, Tome 2015 (2015). http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a47/