Journal
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
Volume 43, Issue 4, Pages 1938-1952Publisher
WILEY
DOI: 10.1002/mma.6017
Keywords
existence and uniqueness; fractional differential equations; fractional integral inequality; stability; psi-Hilfer derivative
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Funding
- Science and Engineering Research Board [EEQ/2018/000407]
- Shivaji University, Kolhapur
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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 the Gronwall inequality, abstract Gronwall lemma, and Picard operator theory are the primary devices in our investigation. We provide an example to illustrate the obtained results.
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