Studies on approximate controllability of fractional differential systems in abstract spaces

Abstract

This thesis has attempted to study the approximate controllability newlinefor the class of control systems governed by the various nonlinear fractional newlineorder differential systems in abstract spaces In particular the problem of newlineapproximate controllability for the fractional integro differential equation is newlineinvestigated by using the Schauder s fixed point theorem Further the set of newlinesufficient conditions for the approximate controllability of nonlinear fractional newlinedifferential equations of order 1 q 2 with nonlocal conditions are established newlinewith the help of solution operator theory Also the result is extended to study the newlineapproximate controllability result for the fractional control system with infinite newlinedelay by using the Schaefers fixed point theorem Moreover in Hilbert spaces newlinethe approximate controllability results for the nonlinear fractional evolution newlineequation with nonlocal conditions are formulated and proved via Schauders newlinefixed point theorem Then by employing the resolvent operator theory the newlineapproximate controllability results are examined for the nonlinear fractional newlineneutral dynamical systems with unbounded delay In addition a new set of newlinesufficient conditions are formulated and proved for achieving the result for the newlineapproximate controllability of a class of impulsive fractional differential newlineequations with infinite delay by using the Krasnoselskii fixed point technique newline newline