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arXiv · 1908.07793

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

Jyoti P. Kharade·Kishor D. Kucche
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Abstract

In this paper, we investigate the existence and uniqueness of solutions and derive the Ulam--Hyers--Mittag--Leffler stability results for impulsive implicit $\Psi$--Hilfer fractional differential equations with time delay. It is demonstrated that the Ulam--Hyers and generalized Ulam--Hyers stability are the specific cases of Ulam--Hyers--Mittag--Leffler stability. Extended version of Gronwall inequality, abstract Gronwall lemma and Picard operator theory are the primary devices in our investigation. We give an example to illustrate the obtained results.

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Jyoti P. Kharade, Kishor D. Kucche. 2019-08-21. On the Impulsive Implicit $\Psi$--Hilfer Fractional Differential Equations with Delay. https://doi.org/10.1002/mma.6017

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