Stability analysis for fractional order implicit ψ‐Hilfer differential equations

The present research endeavor contains formulation of a new ψ‐Hilfer differential equation equipped with integral‐type subsidiary conditions. Utilizing Picard operator method, Banach contraction principle, and Gronwall inequality, we explore solution's properties of the underlying problem. We p...

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Published in:Mathematical methods in the applied sciences 2022-03, Vol.45 (5), p.2701-2712
Main Authors: Asma, Gómez‐Aguilar, José Francisco, Rahman, Ghaus, Javed, Maryam
Format: Article
Language:English
Subjects:
Differential equations
existence of solution
Gronwall inequality
Operators (mathematics)
Stability analysis
Ulam Hyers Mittag Leffler
ψ‐Hilfer derivative
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description The present research endeavor contains formulation of a new ψ‐Hilfer differential equation equipped with integral‐type subsidiary conditions. Utilizing Picard operator method, Banach contraction principle, and Gronwall inequality, we explore solution's properties of the underlying problem. We provide some assumptions to set up results related to uniqueness of solution for the underlying model. Furthermore, stability analysis is studied in the sense of Ulam Hyers Mittag Leffler's definition. We furnish illustrative examples for the vindication of our obtained analytical results.
doi_str_mv 10.1002/mma.7948
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source Wiley-Blackwell Read & Publish Collection
subjects Differential equations
existence of solution
Gronwall inequality
Operators (mathematics)
Stability analysis
Ulam Hyers Mittag Leffler
ψ‐Hilfer derivative
title Stability analysis for fractional order implicit ψ‐Hilfer differential equations
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