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On the Nonlinear Impulsive $\Psi$--Hilfer Fractional Differential Equations

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arxiv 1901.01814 v2 pith:VJ7VFICP submitted 2019-01-07 math.DS math.AP

Kishor D. Kucche , Jyoti P. Kharade , J. Vanterler da C. Sousa This is my paper · ORCID
classification math.DSmath.AP
keywords differentialfractionalhilferimpulsiveresultsequationnonlinearacquired
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abstract

In this paper, we consider the nonlinear $\Psi$-Hilfer impulsive fractional differential equation. Our main objective is to derive the formula for the solution and examine the existence and uniqueness of results. The acquired results are extended to the nonlocal $\Psi$-Hilfer impulsive fractional differential equation. We gave an applications to the outcomes we procured. Further, examples are provided in support of the results we got.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. On the Impulsive Implicit $\Psi$--Hilfer Fractional Differential Equations with Delay

    math.DS 2019-08 reject novelty 4.0 of 10

    The paper claims unique solutions and Ulam-Hyers-Mittag-Leffler stability for implicit impulsive Psi-Hilfer fractional differential equations with delay, but the stability proof relies on a false monotonicity assertion.

  2. Analysis of Impulsive $\varphi$--Hilfer Fractional Differential Equations

    math.DS 2019-08 reject novelty 3.0 of 10

    Extends standard existence, stability, and dependence theorems to impulsive phi-Hilfer fractional differential equations, but the claimed result on dependence on the derivative order is not correctly proved.

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