Ulam–Hyers–Rassias Stability of <i>ψ</i>-Hilfer Volterra Integro-Differential Equations of Fractional Order Containing Multiple Variable Delays
The authors consider a nonlinear <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ψ</mi></semantics></math></inline-formula>-Hilfer fractional-order Volterra integro-differential equat...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-05-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/9/5/304 |
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| Summary: | The authors consider a nonlinear <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ψ</mi></semantics></math></inline-formula>-Hilfer fractional-order Volterra integro-differential equation (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ψ</mi></semantics></math></inline-formula>-Hilfer FrOVIDE) that incorporates <i>N</i>-multiple variable time delays into the equation. By utilizing the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ψ</mi></semantics></math></inline-formula>-Hilfer fractional derivative, they investigate the Ulam–Hyers–Rassias and Ulam–Hyers stability of the equation by using fixed-point methods. Their results improve existing ones both with and without delays by extending them to nonlinear <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ψ</mi></semantics></math></inline-formula>-Hilfer FrOVIDEs that incorporate <i>N</i>-multiple variable time delays. |
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| ISSN: | 2504-3110 |