Existence and Uniqueness Results for a Pantograph Boundary Value Problem Involving a Variable-Order Hadamard Fractional Derivative
This paper discusses the problem of the existence and uniqueness of solutions to the boundary value problem for the nonlinear fractional-order pantograph equation, using the fractional derivative of variable order of Hadamard type. The main results are proved through the application of fractional ca...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-11-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/11/1028 |
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| author | Kadda Maazouz Moussa Daif Allah Zaak Rosana Rodríguez-López |
| author_facet | Kadda Maazouz Moussa Daif Allah Zaak Rosana Rodríguez-López |
| author_sort | Kadda Maazouz |
| collection | DOAJ |
| description | This paper discusses the problem of the existence and uniqueness of solutions to the boundary value problem for the nonlinear fractional-order pantograph equation, using the fractional derivative of variable order of Hadamard type. The main results are proved through the application of fractional calculus and Krasnoselskii’s fixed-point theorem. Moreover, the Ulam–Hyers–Rassias stability of the nonlinear fractional pantograph equation is analyzed. To conclude this paper, we provide an example illustrating our findings and approach. |
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| format | Article |
| id | doaj.art-3c87fac4a19c4b66959c7a51cc426904 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T17:01:25Z |
| publishDate | 2023-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-3c87fac4a19c4b66959c7a51cc4269042023-11-24T14:28:55ZengMDPI AGAxioms2075-16802023-11-011211102810.3390/axioms12111028Existence and Uniqueness Results for a Pantograph Boundary Value Problem Involving a Variable-Order Hadamard Fractional DerivativeKadda Maazouz0Moussa Daif Allah Zaak1Rosana Rodríguez-López2Department of Mathematics, University of Ibn Khaldoun, Tiaret 14000, AlgeriaDepartment of Mathematics, University of Ibn Khaldoun, Tiaret 14000, AlgeriaCITMAga, 15782 Santiago de Compostela, SpainThis paper discusses the problem of the existence and uniqueness of solutions to the boundary value problem for the nonlinear fractional-order pantograph equation, using the fractional derivative of variable order of Hadamard type. The main results are proved through the application of fractional calculus and Krasnoselskii’s fixed-point theorem. Moreover, the Ulam–Hyers–Rassias stability of the nonlinear fractional pantograph equation is analyzed. To conclude this paper, we provide an example illustrating our findings and approach.https://www.mdpi.com/2075-1680/12/11/1028fractional operators of variable orderKrasnoselskii’s fixed-point resultpiecewise continuous functions |
| spellingShingle | Kadda Maazouz Moussa Daif Allah Zaak Rosana Rodríguez-López Existence and Uniqueness Results for a Pantograph Boundary Value Problem Involving a Variable-Order Hadamard Fractional Derivative Axioms fractional operators of variable order Krasnoselskii’s fixed-point result piecewise continuous functions |
| title | Existence and Uniqueness Results for a Pantograph Boundary Value Problem Involving a Variable-Order Hadamard Fractional Derivative |
| title_full | Existence and Uniqueness Results for a Pantograph Boundary Value Problem Involving a Variable-Order Hadamard Fractional Derivative |
| title_fullStr | Existence and Uniqueness Results for a Pantograph Boundary Value Problem Involving a Variable-Order Hadamard Fractional Derivative |
| title_full_unstemmed | Existence and Uniqueness Results for a Pantograph Boundary Value Problem Involving a Variable-Order Hadamard Fractional Derivative |
| title_short | Existence and Uniqueness Results for a Pantograph Boundary Value Problem Involving a Variable-Order Hadamard Fractional Derivative |
| title_sort | existence and uniqueness results for a pantograph boundary value problem involving a variable order hadamard fractional derivative |
| topic | fractional operators of variable order Krasnoselskii’s fixed-point result piecewise continuous functions |
| url | https://www.mdpi.com/2075-1680/12/11/1028 |
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