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)

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

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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