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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MDPI AG
2025-05-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/9/5/304 |
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| author | John R. Graef Osman Tunç Cemil Tunç |
| author_facet | John R. Graef Osman Tunç Cemil Tunç |
| author_sort | John R. Graef |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-ab9acab72dd345f4b7210896c6c12e01 |
| institution | Kabale University |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-ab9acab72dd345f4b7210896c6c12e012025-08-20T03:47:59ZengMDPI AGFractal and Fractional2504-31102025-05-019530410.3390/fractalfract9050304Ulam–Hyers–Rassias Stability of <i>ψ</i>-Hilfer Volterra Integro-Differential Equations of Fractional Order Containing Multiple Variable DelaysJohn R. Graef0Osman Tunç1Cemil Tunç2Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, USADepartment of Computer Programming, Baskale Vocational School, Van Yuzuncu Yil University, Van 65080, TurkeyDepartment of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, Van 65080, TurkeyThe 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.https://www.mdpi.com/2504-3110/9/5/304Hilfer fractional-order Volterra integro-differential equationsUlam–Hyers–Rassias stabilityUlam–Hyers stabilityfixed-point methods |
| spellingShingle | John R. Graef Osman Tunç Cemil Tunç Ulam–Hyers–Rassias Stability of <i>ψ</i>-Hilfer Volterra Integro-Differential Equations of Fractional Order Containing Multiple Variable Delays Fractal and Fractional Hilfer fractional-order Volterra integro-differential equations Ulam–Hyers–Rassias stability Ulam–Hyers stability fixed-point methods |
| title | Ulam–Hyers–Rassias Stability of <i>ψ</i>-Hilfer Volterra Integro-Differential Equations of Fractional Order Containing Multiple Variable Delays |
| title_full | Ulam–Hyers–Rassias Stability of <i>ψ</i>-Hilfer Volterra Integro-Differential Equations of Fractional Order Containing Multiple Variable Delays |
| title_fullStr | Ulam–Hyers–Rassias Stability of <i>ψ</i>-Hilfer Volterra Integro-Differential Equations of Fractional Order Containing Multiple Variable Delays |
| title_full_unstemmed | Ulam–Hyers–Rassias Stability of <i>ψ</i>-Hilfer Volterra Integro-Differential Equations of Fractional Order Containing Multiple Variable Delays |
| title_short | Ulam–Hyers–Rassias Stability of <i>ψ</i>-Hilfer Volterra Integro-Differential Equations of Fractional Order Containing Multiple Variable Delays |
| title_sort | ulam hyers rassias stability of i ψ i hilfer volterra integro differential equations of fractional order containing multiple variable delays |
| topic | Hilfer fractional-order Volterra integro-differential equations Ulam–Hyers–Rassias stability Ulam–Hyers stability fixed-point methods |
| url | https://www.mdpi.com/2504-3110/9/5/304 |
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