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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Main Authors: Ahmed M. A. El-Sayed, Wagdy G. El-Sayed, Kheria M. O. Msaik, Hanaa R. Ebead
Format: Article
Language:English
Published: AIMS Press 2025-03-01
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.
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institution DOAJ
issn 2473-6988
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publisher AIMS Press
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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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AT kheriamomsaik riemannliouvillefractionalorderpantographdifferentialequationconstrainedbynonlocalandweightedpantographintegralequations
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