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

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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.

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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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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247667, India

    Kamal Jeet & N. Sukavanam

  2. Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur, 208016, India

    D. Bahuguna

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  1. Kamal Jeet
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  2. N. Sukavanam
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  3. D. Bahuguna
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Correspondence to Kamal Jeet.

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Jeet, K., Sukavanam, N. & Bahuguna, D. Monotone Iterative Technique for Nonlocal Impulsive Finite Delay Differential Equations of Fractional Order. Differ Equ Dyn Syst 30, 801–816 (2022). https://doi.org/10.1007/s12591-019-00498-4

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