Riemann-Liouville fractional-order pantograph differential equation constrained by nonlocal and weighted pantograph integral equations
In this research, we investigated the Riemann-Liouville fractional-order pantograph differential equation constrained by nonlocal and weighted pantograph integral constraints. We presented novel sufficient conditions for the uniqueness of the solution. Moreover, we analyzed the continuous dependence...
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| Format: | Article |
| Language: | English |
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AIMS Press
2025-03-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025228 |
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| author | Ahmed M. A. El-Sayed Wagdy G. El-Sayed Kheria M. O. Msaik Hanaa R. Ebead |
| author_facet | Ahmed M. A. El-Sayed Wagdy G. El-Sayed Kheria M. O. Msaik Hanaa R. Ebead |
| author_sort | Ahmed M. A. El-Sayed |
| collection | DOAJ |
| description | In this research, we investigated the Riemann-Liouville fractional-order pantograph differential equation constrained by nonlocal and weighted pantograph integral constraints. We presented novel sufficient conditions for the uniqueness of the solution. Moreover, we analyzed the continuous dependence of the solution on some functions and parameters. Additionally, we proved the Hyers-Ulam stability of the problem. To demonstrate the applicability of our results, we included several examples. The present study was located in the space $ L_1[0, T] $. The techniques of Schauder's fixed point theorem and Kolmogorov's compactness criterion were the primary tools utilized in this work. These contributions offer a comprehensive framework for understanding the qualitative behavior of the fractional-order pantograph equation. |
| format | Article |
| id | doaj-art-805f2dec7fa641788ca6a3ccbff4e421 |
| institution | DOAJ |
| issn | 2473-6988 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-805f2dec7fa641788ca6a3ccbff4e4212025-08-20T03:16:57ZengAIMS PressAIMS Mathematics2473-69882025-03-011034970499110.3934/math.2025228Riemann-Liouville fractional-order pantograph differential equation constrained by nonlocal and weighted pantograph integral equationsAhmed M. A. El-Sayed0Wagdy G. El-Sayed1Kheria M. O. Msaik2Hanaa R. Ebead3Department of Mathematics, Faculty of Science, Alexandria University, Alexandria, EgyptDepartment of Mathematics, Faculty of Science, Alexandria University, Alexandria, EgyptDepartment of Mathematics, Faculty of Science, Zintan University, Zintan, LibyaDepartment of Mathematics, Faculty of Science, Alexandria University, Alexandria, EgyptIn this research, we investigated the Riemann-Liouville fractional-order pantograph differential equation constrained by nonlocal and weighted pantograph integral constraints. We presented novel sufficient conditions for the uniqueness of the solution. Moreover, we analyzed the continuous dependence of the solution on some functions and parameters. Additionally, we proved the Hyers-Ulam stability of the problem. To demonstrate the applicability of our results, we included several examples. The present study was located in the space $ L_1[0, T] $. The techniques of Schauder's fixed point theorem and Kolmogorov's compactness criterion were the primary tools utilized in this work. These contributions offer a comprehensive framework for understanding the qualitative behavior of the fractional-order pantograph equation.https://www.aimspress.com/article/doi/10.3934/math.2025228pantograph differential equationschauder fixed point theoremweighted pantograph integral equationnonlocal conditionsriemann-liouville fractional derivativecontinuous dependencehyers-ulam stability |
| spellingShingle | Ahmed M. A. El-Sayed Wagdy G. El-Sayed Kheria M. O. Msaik Hanaa R. Ebead Riemann-Liouville fractional-order pantograph differential equation constrained by nonlocal and weighted pantograph integral equations AIMS Mathematics pantograph differential equation schauder fixed point theorem weighted pantograph integral equation nonlocal conditions riemann-liouville fractional derivative continuous dependence hyers-ulam stability |
| title | Riemann-Liouville fractional-order pantograph differential equation constrained by nonlocal and weighted pantograph integral equations |
| title_full | Riemann-Liouville fractional-order pantograph differential equation constrained by nonlocal and weighted pantograph integral equations |
| title_fullStr | Riemann-Liouville fractional-order pantograph differential equation constrained by nonlocal and weighted pantograph integral equations |
| title_full_unstemmed | Riemann-Liouville fractional-order pantograph differential equation constrained by nonlocal and weighted pantograph integral equations |
| title_short | Riemann-Liouville fractional-order pantograph differential equation constrained by nonlocal and weighted pantograph integral equations |
| title_sort | riemann liouville fractional order pantograph differential equation constrained by nonlocal and weighted pantograph integral equations |
| topic | pantograph differential equation schauder fixed point theorem weighted pantograph integral equation nonlocal conditions riemann-liouville fractional derivative continuous dependence hyers-ulam stability |
| url | https://www.aimspress.com/article/doi/10.3934/math.2025228 |
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