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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"&g...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-02-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/7/2/162 |
| _version_ | 1797620921374081024 |
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| author | Mohammed S. Abdo Wafa Shammakh Hadeel Z. Alzumi Najla Alghamd M. Daher Albalwi |
| author_facet | Mohammed S. Abdo Wafa Shammakh Hadeel Z. Alzumi Najla Alghamd M. Daher Albalwi |
| author_sort | Mohammed S. Abdo |
| collection | DOAJ |
| description | 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mi>s</mi><mi>i</mi></mrow></semantics></math></inline-formula>-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. |
| first_indexed | 2024-03-11T08:49:24Z |
| format | Article |
| id | doaj.art-f57caf32231f44d19bf130374f5544a9 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-11T08:49:24Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-f57caf32231f44d19bf130374f5544a92023-11-16T20:36:50ZengMDPI AGFractal and Fractional2504-31102023-02-017216210.3390/fractalfract7020162Nonlinear Piecewise Caputo Fractional Pantograph System with Respect to Another FunctionMohammed S. Abdo0Wafa Shammakh1Hadeel Z. Alzumi2Najla Alghamd3M. Daher Albalwi4Department of Mathematics, Hodeidah University, Al-Hudaydah 3114, YemenDepartment of Mathematics, Faculty of Science, University of Jeddah, Jeddah 23218, Saudi ArabiaDepartment of Mathematics, Faculty of Science, University of Jeddah, Jeddah 23218, Saudi ArabiaDepartment of Mathematics, Faculty of Science, University of Jeddah, Jeddah 23218, Saudi ArabiaYanbu Industrial College, The Royal Commission for Jubail and Yanbu, Yanbu 30436, Saudi ArabiaThe 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mi>s</mi><mi>i</mi></mrow></semantics></math></inline-formula>-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.https://www.mdpi.com/2504-3110/7/2/162pantograph equationpiecewise fractional derivativefixed point theorem |
| spellingShingle | Mohammed S. Abdo Wafa Shammakh Hadeel Z. Alzumi Najla Alghamd M. Daher Albalwi Nonlinear Piecewise Caputo Fractional Pantograph System with Respect to Another Function Fractal and Fractional pantograph equation piecewise fractional derivative fixed point theorem |
| title | Nonlinear Piecewise Caputo Fractional Pantograph System with Respect to Another Function |
| title_full | Nonlinear Piecewise Caputo Fractional Pantograph System with Respect to Another Function |
| title_fullStr | Nonlinear Piecewise Caputo Fractional Pantograph System with Respect to Another Function |
| title_full_unstemmed | Nonlinear Piecewise Caputo Fractional Pantograph System with Respect to Another Function |
| title_short | Nonlinear Piecewise Caputo Fractional Pantograph System with Respect to Another Function |
| title_sort | nonlinear piecewise caputo fractional pantograph system with respect to another function |
| topic | pantograph equation piecewise fractional derivative fixed point theorem |
| url | https://www.mdpi.com/2504-3110/7/2/162 |
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