Relative controllability results for nonlinear higher order fractional delay integrodifferential systems with time varying delay in control

Abstract

This paper is concerned with the controllability of nonlinear higher order fractional delay integrodifferential equations with time varying delay in control, which involved Caputo derivatives of any different orders. A formula for the solution expression of the system is derived by using Laplace transform. A necessary and sufficient condition for the relative controllability of linear fractional delay dynamical systems with time varying delays in control is proved, and a sufficient condition for the corresponding nonlinear integrodifferential equation has obtained. Examples has given to verify the results.

Keywords

• Fractional delay integrodifferential equation,relative controllability,Laplace transform,Mittag-Leffler matrix function,Schaefer's fixed point theorem

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