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Monotone Iterative Technique for Nonlocal Impulsive Finite Delay Differential Equations of Fractional Order

  • Kamal JeetEmail author
  • N. Sukavanam
  • D. Bahuguna
Original Research
  • 37 Downloads

Abstract

The paper is concerned with the extension of a monotone iterative technique to impulsive finite delay differential equations of fractional order with a nonlocal initial condition in an ordered Banach space. We study the existence of extremal mild solutions with or without assuming the compactness of a semigroup and also prove the uniqueness of the mild solution of the system. The results are obtained with the help of fractional calculus, a measure of non-compactness, the semigroup theory and monotone iterative technique. Finally, an example is provided to show the application of our main.

Keywords

Impulsive fractional differential equations Finite delay Semigroup theory Monotone iterative technique Lower and upper solutions Kuratowskii measure of noncompactness 

Mathematics Subject Classification

34A08 34G20 34K30 93B05 

Notes

Acknowledgements

The authors would like to thank the referees for their valuable comments and suggestions which improved the quality of the manuscript. Kamal Jeet would like to acknowledge DST-SERB, India for carrying out this research work under the research project PDF/2016/003875.

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Copyright information

© Foundation for Scientific Research and Technological Innovation 2019

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology RoorkeeRoorkeeIndia
  2. 2.Department of Mathematics and StatisticsIndian Institute of Technology KanpurKanpurIndia

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