Discontinuity, Nonlinearity, and Complexity 11(3) (2022) 459--472 | 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

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 convex-power 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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