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 higherorder fractional delay integrodi§erential equations with time varying delay incontrol, which involved Caputo derivatives of any di§erent orders. A formulafor the solution expression of the system is derived by using Laplace transform. A necessary and su¢ cient condition for the relative controllability oflinear fractional delay dynamical systems with time varying delays in controlis proved, and a su¢ cient condition for the corresponding nonlinear integrodi§erential equation has obtained. Examples has given to verify the results.