A novel approach to Caputo–Hadamard pantograph problems in L p $\mathfrak{L}^{\mathsf{p}}$ -spaces
Abstract In this paper, we investigate the existence and uniqueness of solutions for Caputo–Hadamard pantograph fractional differential equations with boundary conditions in L p $\mathfrak{L}^{\mathsf{p}}$ -spaces, by applying fixed-point theorems in L p $\mathfrak{L}^{\mathsf{p}}$ -spaces to prove...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-05-01
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| Series: | Boundary Value Problems |
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| Online Access: | https://doi.org/10.1186/s13661-025-02054-2 |
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| author | Gunaseelan Mani Purushothaman Ganesh Kokila Kannan Maryam Ali Alghafli Nabil Mlaiki |
| author_facet | Gunaseelan Mani Purushothaman Ganesh Kokila Kannan Maryam Ali Alghafli Nabil Mlaiki |
| author_sort | Gunaseelan Mani |
| collection | DOAJ |
| description | Abstract In this paper, we investigate the existence and uniqueness of solutions for Caputo–Hadamard pantograph fractional differential equations with boundary conditions in L p $\mathfrak{L}^{\mathsf{p}}$ -spaces, by applying fixed-point theorems in L p $\mathfrak{L}^{\mathsf{p}}$ -spaces to prove existence and uniqueness. Stability is analyzed through the Ulam–Hyers stability and Ulam–Hyers–Rassias stability, offering key insights into the reliability of the system. Practical examples are also provided for illustration. |
| format | Article |
| id | doaj-art-7658a3a93be844ed8485a5b211da52d6 |
| institution | Kabale University |
| issn | 1687-2770 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj-art-7658a3a93be844ed8485a5b211da52d62025-08-20T03:53:13ZengSpringerOpenBoundary Value Problems1687-27702025-05-012025112310.1186/s13661-025-02054-2A novel approach to Caputo–Hadamard pantograph problems in L p $\mathfrak{L}^{\mathsf{p}}$ -spacesGunaseelan Mani0Purushothaman Ganesh1Kokila Kannan2Maryam Ali Alghafli3Nabil Mlaiki4Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha UniversityDepartment of Mathematics, St. Joseph’s College of EngineeringDepartment of Mathematics, K. Ramakrishnan College of Engineering (Autonomous)Department of Mathematics and Sciences, Prince Sultan UniversityDepartment of Mathematics and Sciences, Prince Sultan UniversityAbstract In this paper, we investigate the existence and uniqueness of solutions for Caputo–Hadamard pantograph fractional differential equations with boundary conditions in L p $\mathfrak{L}^{\mathsf{p}}$ -spaces, by applying fixed-point theorems in L p $\mathfrak{L}^{\mathsf{p}}$ -spaces to prove existence and uniqueness. Stability is analyzed through the Ulam–Hyers stability and Ulam–Hyers–Rassias stability, offering key insights into the reliability of the system. Practical examples are also provided for illustration.https://doi.org/10.1186/s13661-025-02054-2Caputo–HadamardFractional derivativesFractional integralFixed pointBanach contraction |
| spellingShingle | Gunaseelan Mani Purushothaman Ganesh Kokila Kannan Maryam Ali Alghafli Nabil Mlaiki A novel approach to Caputo–Hadamard pantograph problems in L p $\mathfrak{L}^{\mathsf{p}}$ -spaces Boundary Value Problems Caputo–Hadamard Fractional derivatives Fractional integral Fixed point Banach contraction |
| title | A novel approach to Caputo–Hadamard pantograph problems in L p $\mathfrak{L}^{\mathsf{p}}$ -spaces |
| title_full | A novel approach to Caputo–Hadamard pantograph problems in L p $\mathfrak{L}^{\mathsf{p}}$ -spaces |
| title_fullStr | A novel approach to Caputo–Hadamard pantograph problems in L p $\mathfrak{L}^{\mathsf{p}}$ -spaces |
| title_full_unstemmed | A novel approach to Caputo–Hadamard pantograph problems in L p $\mathfrak{L}^{\mathsf{p}}$ -spaces |
| title_short | A novel approach to Caputo–Hadamard pantograph problems in L p $\mathfrak{L}^{\mathsf{p}}$ -spaces |
| title_sort | novel approach to caputo hadamard pantograph problems in l p mathfrak l mathsf p spaces |
| topic | Caputo–Hadamard Fractional derivatives Fractional integral Fixed point Banach contraction |
| url | https://doi.org/10.1186/s13661-025-02054-2 |
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