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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com


Impulsive Functional-Controllability Problem for Fractional Integro-Differential Evolution Systems of Mixed Type with the Measure of Noncompactness

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

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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 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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