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Existence of the Mild Solutions for Impulsive Fractional Equations with Infinite Delay

Author

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  • Jaydev Dabas
  • Archana Chauhan
  • Mukesh Kumar

Abstract

This paper is concerned with the existence and uniqueness of a mild solution of a semilinear fractional-order functional evolution differential equation with the infinite delay and impulsive effects. The existence and uniqueness of a mild solution is established using a solution operator and the classical fixed-point theorems.

Suggested Citation

  • Jaydev Dabas & Archana Chauhan & Mukesh Kumar, 2011. "Existence of the Mild Solutions for Impulsive Fractional Equations with Infinite Delay," International Journal of Differential Equations, Hindawi, vol. 2011, pages 1-20, October.
    • Handle: RePEc:hin:jnijde:793023
    DOI: 10.1155/2011/793023
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    Cited by:

    1. Selvaraj Suganya & Mani Mallika Arjunan, 2017. "Existence of Mild Solutions for Impulsive Fractional Integro-Differential Inclusions with State-Dependent Delay," Mathematics, MDPI, vol. 5(1), pages 1-16, January.
    2. Suganya, S. & Mallika Arjunan, M. & Trujillo, J.J., 2015. "Existence results for an impulsive fractional integro-differential equation with state-dependent delay," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 54-69.
    3. Sousa, J. Vanterler da C. & Oliveira, D.S. & Capelas de Oliveira, E., 2021. "A note on the mild solutions of Hilfer impulsive fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).

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