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Sufficient Conditions for Existence of Integral Solution for Non-Instantaneous Impulsive Fractional Evolution Equations

Author

Listed:
  • Jayanta Borah

    (Indian Institute of Technology Guwahati)

  • Swaroop Nandan Bora

    (Indian Institute of Technology Guwahati)

Abstract

In this article, we establish sufficient conditions for existence and uniqueness of integral solution for some non-densely defined non-instantaneous impulsive evolution equations on a Banach space involving Caputo fractional derivative. The results are obtained by means of characteristic functions based on probability density. Finally, the main results are illustrated through examples.

Suggested Citation

  • Jayanta Borah & Swaroop Nandan Bora, 2020. "Sufficient Conditions for Existence of Integral Solution for Non-Instantaneous Impulsive Fractional Evolution Equations," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(3), pages 1065-1082, September.
    • Handle: RePEc:spr:indpam:v:51:y:2020:i:3:d:10.1007_s13226-020-0450-4
    DOI: 10.1007/s13226-020-0450-4
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    References listed on IDEAS

    as
    1. Gautam, Ganga Ram & Dabas, Jaydev, 2015. "Mild solutions for class of neutral fractional functional differential equations with not instantaneous impulses," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 480-489.
    2. Zufeng Zhang & Bin Liu, 2012. "A Note on Impulsive Fractional Evolution Equations with Nondense Domain," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-13, August.
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