Nonlinear Piecewise Caputo Fractional Pantograph System with Respect to Another Function

The existence, uniqueness, and various forms of Ulam–Hyers (UH)-type stability results for nonlocal pantograph equations are developed and extended in this study within the frame of novel psi-piecewise Caputo fractional derivatives, which generalize the piecewise operators recently presented in the...

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Bibliographic Details
Published in:Fractal and fractional 2023-02, Vol.7 (2), p.162
Main Authors: Abdo, Mohammed S., Shammakh, Wafa, Alzumi, Hadeel Z., Alghamd, Najla, Albalwi, M. Daher
Format: Article
Language:English
Subjects:
fixed point theorem
Fixed points (mathematics)
Functional analysis
Mathematical functions
Operators (mathematics)
pantograph equation
Pantographs
piecewise fractional derivative
Stability analysis
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Summary:The existence, uniqueness, and various forms of Ulam–Hyers (UH)-type stability results for nonlocal pantograph equations are developed and extended in this study within the frame of novel psi-piecewise Caputo fractional derivatives, which generalize the piecewise operators recently presented in the literature. The required results are proven using Banach’s contraction mapping and Krasnoselskii’s fixed-point theorem. Additionally, results pertaining to UH stability are obtained using traditional procedures of nonlinear functional analysis. Additionally, in light of our current findings, a more general challenge for the pantograph system is presented that includes problems similar to the one considered. We provide a pertinent example as an application to support the theoretical findings.
ISSN:2504-3110
2504-3110
DOI:10.3390/fractalfract7020162