Controllability of fractional impulsive quasilinear differential systems with state dependent delay

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Abstract

In this paper, we study some controllability results for an abstract fractional impulsive quasilinear integro-differential system with state-dependent delay. We will use the concepts of fractional calculus, measure of noncompactness and abstract phase space to come up with a new set of sufficient conditions for controllability by using Mönch’s fixed point theorem. Finally, an application is given to illustrate the obtained results.

Keywords

Controllability Fractional impulsive quasilinear integro-differential system \((\alpha , y)\)-resolvent family Mönch’s fixed point theorem State-dependent delay Measure of noncompactness 

Mathematics Subject Classification

26A33 34A08 34A37 34G20 34K30 35R12 47H10 47H08 93B05 

Notes

Acknowledgements

The work of the first author is supported by the “Ministry of Human Resource and Development, India under Grant number: MHR-02-23-200-44”.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology RoorkeeRoorkeeIndia

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