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Analysis of Impulsive \(\varphi \)–Hilfer Fractional Differential Equations

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Abstract

This paper is concerned with the existence and uniqueness, and Ulam–Hyers stabilities of solutions of nonlinear impulsive \(\varphi \)–Hilfer fractional differential equations. Further, we investigate the dependence of the solution on the initial conditions, order of derivative and the functions involved in the equations. The outcomes are acquired in the space of weighted piecewise continuous functions by means of fixed point theorems and the generalized version of Gronwall inequality.

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Acknowledgements

The first author acknowledges the Science and Engineering Research Board (SERB), New Delhi, India for the Research Grant (Ref: File No. EEQ/2018/000407).

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  1. Department of Mathematics, Shivaji University, Kolhapur, Maharashtra, 416 004, India

    Kishor D. Kucche & Jyoti P. Kharade

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  1. Kishor D. Kucche
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  2. Jyoti P. Kharade
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Correspondence to Kishor D. Kucche.

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Kucche, K.D., Kharade, J.P. Analysis of Impulsive \(\varphi \)–Hilfer Fractional Differential Equations. Mediterr. J. Math. 17, 163 (2020). https://doi.org/10.1007/s00009-020-01575-7

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  • DOI: https://doi.org/10.1007/s00009-020-01575-7

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