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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

A Class of Nonlocal Fractional Evolution Equations and Optimal Controls

Journal of Applied Nonlinear Dynamics 6(4) (2017) 445--463 | DOI:10.5890/JAND.2017.12.001

Ravi P. Agarwal$^{1}$, Asma$^{2}$, Vasile Lupulescu$^{3}$, Donal O’Regan$^{4}$

$^{1}$ Department of Mathematics, Texas A&M University-Kingvsille, Kingsville, USA

$^{2}$ Abdus Salam School of Mathematical Sciences, GCU, Lahore, Pakistan

$^{3}$ University Constantin Brâncusi, Str. Geneva, Nr. 3, 210136 Târgu-Jiu, România

$^{4}$ School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, University Road, Galway, Ireland

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Abstract

In this paper we study the existence of solutions for a class of semilinear fractional differential equations with nonlocal conditions and involving abstract Volterra operators. The existence of an optimal solution for a class of fractional control problem involving Caputo fractional derivatives is obtained. An example is presented to illustrate our main result.

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