Discontinuity, Nonlinearity, and Complexity
Impulsive FunctionalControllability Problem for Fractional IntegroDifferential Evolution Systems of Mixed Type with the Measure of Noncompactness
Discontinuity, Nonlinearity, and Complexity 11(3) (2022) 459472  DOI:10.5890/DNC.2022.09.008
K. Karthikeyan$^1$, D. Senthil Raja$^2$, P. Sundararajan$^3$
$^1$ Department of Mathematics & Centre for Research and Development, KPR Institute of Engineering and
Technology, Coimbatore  641 407, Tamil Nadu, India
$^2$ Department of Mathematics, K.S.Rangasamy College of Technology, Tiruchengode  637 215, Tamil Nadu,
India
$^3$ Department of Mathematics, Arignar Anna Government Arts College, Namakkal 
637 002, Tamil Nadu, India
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Abstract
We consider the controllability problem for a class of fractional impulsive evolution systems of mixed type in an infinite dimensional Banach space. The existence of mild solutions and controllability results are discussed by a new estimation technique of the measure of noncompactness and a fixed point theorem with respect to a convexpower condensing operator. However, the main results do not need any restrictive conditions on estimated parameters of the measure of noncompactness. Since we do not assume that the semigroup is compact and other conditions are more general, the outcomes we obtain here improve and generalize many known controllability results. An example is also given to demonstrate the applications of our main results.
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