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PC-Mild Solutions to Sobolev-Type Fractional Differential Equations with Non-instantaneous Impulses

  • Vikram SinghEmail author
  • Dwijendra N. Pandey
Article
  • 63 Downloads

Abstract

In this paper, we study the existence and uniqueness of piecewise-continuous (in brief, PC)-mild solutions for Sobolev-type fractional impulsive differential equations (in brief, STFIDEs) with state-dependent delay by virtue of Kuratowski measure of noncompactness in a Banach space. We establish a general framework to find PC-mild solutions for STFIDEs with compact and noncompact semigroups, which will provide an effective way to deal with such problems. Finally, an application is given to illustrate that our results are valuable.

Keywords

Fractional calculus Sobolev-type fractional impulsive differential equations Measure of noncompactness PC-mild solutions not-instantaneous impulses State-dependent delay 

Mathematics Subject Classification

26A33 34A08 34A12 34A37 34G20 35R11 35R12 

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 Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Indian Institute of Technology RoorkeeRoorkeeIndia

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