An Exploration of the Qualitative Analysis of the Generalized Pantograph Equation with the <i>q</i>-Hilfer Fractional Derivative
This manuscript tries to show that there is only one solution to the problem of the q-Hilfer fractional generalized pantograph differential equations with a nonlocal condition, and it does so by employing a particular technique known as Schaefer’s fixed point theorem and the Banach contraction princ...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-05-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/9/5/302 |
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| author | R. Vivek K. Kanagarajan D. Vivek T. D. Alharbi E. M. Elsayed |
| author_facet | R. Vivek K. Kanagarajan D. Vivek T. D. Alharbi E. M. Elsayed |
| author_sort | R. Vivek |
| collection | DOAJ |
| description | This manuscript tries to show that there is only one solution to the problem of the q-Hilfer fractional generalized pantograph differential equations with a nonlocal condition, and it does so by employing a particular technique known as Schaefer’s fixed point theorem and the Banach contraction principle. Then, we verify that the Ulam-type stability is valid. To illustrate the results, an example is provided. |
| format | Article |
| id | doaj-art-1f171f67e6ed4adeb3d9815c2bbb9752 |
| institution | OA Journals |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-1f171f67e6ed4adeb3d9815c2bbb97522025-08-20T01:56:24ZengMDPI AGFractal and Fractional2504-31102025-05-019530210.3390/fractalfract9050302An Exploration of the Qualitative Analysis of the Generalized Pantograph Equation with the <i>q</i>-Hilfer Fractional DerivativeR. Vivek0K. Kanagarajan1D. Vivek2T. D. Alharbi3E. M. Elsayed4Department of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore 641020, IndiaDepartment of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore 641020, IndiaDepartment of Mathematics, PSG College of Arts & Science, Coimbatore 641014, IndiaDepartment of Mathematics, Al-Leith University College, Umm Al-Qura University, Mecca 24382, Saudi ArabiaDepartment of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21859, Saudi ArabiaThis manuscript tries to show that there is only one solution to the problem of the q-Hilfer fractional generalized pantograph differential equations with a nonlocal condition, and it does so by employing a particular technique known as Schaefer’s fixed point theorem and the Banach contraction principle. Then, we verify that the Ulam-type stability is valid. To illustrate the results, an example is provided.https://www.mdpi.com/2504-3110/9/5/302q-Hilfer fractional derivativepantograph equationexistenceuniquenessUlam stablenonlocal condition |
| spellingShingle | R. Vivek K. Kanagarajan D. Vivek T. D. Alharbi E. M. Elsayed An Exploration of the Qualitative Analysis of the Generalized Pantograph Equation with the <i>q</i>-Hilfer Fractional Derivative Fractal and Fractional q-Hilfer fractional derivative pantograph equation existence uniqueness Ulam stable nonlocal condition |
| title | An Exploration of the Qualitative Analysis of the Generalized Pantograph Equation with the <i>q</i>-Hilfer Fractional Derivative |
| title_full | An Exploration of the Qualitative Analysis of the Generalized Pantograph Equation with the <i>q</i>-Hilfer Fractional Derivative |
| title_fullStr | An Exploration of the Qualitative Analysis of the Generalized Pantograph Equation with the <i>q</i>-Hilfer Fractional Derivative |
| title_full_unstemmed | An Exploration of the Qualitative Analysis of the Generalized Pantograph Equation with the <i>q</i>-Hilfer Fractional Derivative |
| title_short | An Exploration of the Qualitative Analysis of the Generalized Pantograph Equation with the <i>q</i>-Hilfer Fractional Derivative |
| title_sort | exploration of the qualitative analysis of the generalized pantograph equation with the i q i hilfer fractional derivative |
| topic | q-Hilfer fractional derivative pantograph equation existence uniqueness Ulam stable nonlocal condition |
| url | https://www.mdpi.com/2504-3110/9/5/302 |
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