Title: Controllability of nonlocal fractional functional differential equations of neutral type in a Banach space

Authors: Madhukant Sharma; Shruti Dubey

Addresses: Department of Mathematics, Indian Institute of Technology Madras, Chennai 600 036, India ' Department of Mathematics, Indian Institute of Technology Madras, Chennai 600 036, India

Abstract: This paper is concerned with the controllability of nonlinear nonlocal fractional neutral functional evolution system in a Banach space. Sufficient conditions are obtained by using Krasnoselskii's fixed point theorem and semigroup theory. In particular, we assume that the nonlinear parts satisfy locally Lipschitz like conditions and closed linear (not necessarily bounded) operator −A(t) generates analytic semigroup for each t ≥ 0. We also investigate null controllability of the considered system. An example is given to illustrate the effectiveness of our results.

Keywords: neutral functional differential equations; fractional calculus; complete controllability; null controllability; analytic semigroups; fractional power; operators; Banach space; fixed point theorem.

DOI: 10.1504/IJDSDE.2015.072840

International Journal of Dynamical Systems and Differential Equations, 2015 Vol.5 No.4, pp.302 - 321

Available online: 04 Nov 2015 *

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