Exploring the solutions of tempered (κ,ϖ)-Hilfer hybrid implicit boundary value problem
In this manuscript, we provide an in-depth analysis of existence and uniqueness results, along with stability assessments associated with the κ-Mittag-Leffler-Ulam-Hyers type, specifically focusing on a newly formulated category of hybrid boundary value problems (BVPs) that incorporate fractional de...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-04-01
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| Series: | Alexandria Engineering Journal |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016825000973 |
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| author | Abdelkrim Salim Sabri T.M. Thabet Ava Sh. Rafeeq Mohammad Esmael Samei Imed Kedim Miguel Vivas-Cortez |
| author_facet | Abdelkrim Salim Sabri T.M. Thabet Ava Sh. Rafeeq Mohammad Esmael Samei Imed Kedim Miguel Vivas-Cortez |
| author_sort | Abdelkrim Salim |
| collection | DOAJ |
| description | In this manuscript, we provide an in-depth analysis of existence and uniqueness results, along with stability assessments associated with the κ-Mittag-Leffler-Ulam-Hyers type, specifically focusing on a newly formulated category of hybrid boundary value problems (BVPs) that incorporate fractional derivatives. Our study leverages the properties of tempered (κ,ϖ)-Hilfer fractional operators to explore the mathematical underpinnings of the problem, which is characterized by implicit nonlinear fractional differential equations. To derive the results, we employ Banach’s fixed point theorem, which facilitates the demonstration of the existence of solutions under certain contractive conditions. We also utilize a generalized Gronwall inequality to establish bounds and stability criteria for the solutions, thereby ensuring their robustness under perturbations. Moreover, we underscore the practical applicability of our theoretical findings by presenting several illustrative examples. These examples not only help demonstrate the effectiveness of our approach but also highlight the relevance of the results in addressing real-world scenarios where fractional dynamics are pertinent. |
| format | Article |
| id | doaj-art-5f72db399e794195ab49d2ffaced1523 |
| institution | Kabale University |
| issn | 1110-0168 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj-art-5f72db399e794195ab49d2ffaced15232025-02-06T05:11:11ZengElsevierAlexandria Engineering Journal1110-01682025-04-01119138148Exploring the solutions of tempered (κ,ϖ)-Hilfer hybrid implicit boundary value problemAbdelkrim Salim0Sabri T.M. Thabet1Ava Sh. Rafeeq2Mohammad Esmael Samei3Imed Kedim4Miguel Vivas-Cortez5Faculty of Technology, Hassiba Benbouali University of Chlef, P.O. Box 151, Chlef 02000, Algeria; Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbes, P.O. Box 89, Sidi Bel-Abbes 22000, AlgeriaDepartment of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai 602105, Tamil Nadu, India; Department of Mathematics, Radfan University College, University of Lahej, Lahej, Yemen; Department of Mathematics, College of Science, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul 02814, Republic of Korea; Corresponding authors.Department of Mathematics, College of Science, University of Zakho, Duhok, IraqDepartment of Mathematics, Faculty of Science, Bu-Ali Sina University, Hamedan, IranDepartment of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi ArabiaFaculty of Exact and Natural Sciences, School of Physical Sciences and Mathematics, Pontifical Catholic University of Ecuador, Sede Quito, Ecuador; Corresponding authors.In this manuscript, we provide an in-depth analysis of existence and uniqueness results, along with stability assessments associated with the κ-Mittag-Leffler-Ulam-Hyers type, specifically focusing on a newly formulated category of hybrid boundary value problems (BVPs) that incorporate fractional derivatives. Our study leverages the properties of tempered (κ,ϖ)-Hilfer fractional operators to explore the mathematical underpinnings of the problem, which is characterized by implicit nonlinear fractional differential equations. To derive the results, we employ Banach’s fixed point theorem, which facilitates the demonstration of the existence of solutions under certain contractive conditions. We also utilize a generalized Gronwall inequality to establish bounds and stability criteria for the solutions, thereby ensuring their robustness under perturbations. Moreover, we underscore the practical applicability of our theoretical findings by presenting several illustrative examples. These examples not only help demonstrate the effectiveness of our approach but also highlight the relevance of the results in addressing real-world scenarios where fractional dynamics are pertinent.http://www.sciencedirect.com/science/article/pii/S1110016825000973Hybrid implicit equationsTempered (κ, ϖ)-hilfer fractional operatorsMittag-leffler-ulam-hyers stabilityGeneralized gronwall inequality |
| spellingShingle | Abdelkrim Salim Sabri T.M. Thabet Ava Sh. Rafeeq Mohammad Esmael Samei Imed Kedim Miguel Vivas-Cortez Exploring the solutions of tempered (κ,ϖ)-Hilfer hybrid implicit boundary value problem Alexandria Engineering Journal Hybrid implicit equations Tempered (κ, ϖ)-hilfer fractional operators Mittag-leffler-ulam-hyers stability Generalized gronwall inequality |
| title | Exploring the solutions of tempered (κ,ϖ)-Hilfer hybrid implicit boundary value problem |
| title_full | Exploring the solutions of tempered (κ,ϖ)-Hilfer hybrid implicit boundary value problem |
| title_fullStr | Exploring the solutions of tempered (κ,ϖ)-Hilfer hybrid implicit boundary value problem |
| title_full_unstemmed | Exploring the solutions of tempered (κ,ϖ)-Hilfer hybrid implicit boundary value problem |
| title_short | Exploring the solutions of tempered (κ,ϖ)-Hilfer hybrid implicit boundary value problem |
| title_sort | exploring the solutions of tempered κ ϖ hilfer hybrid implicit boundary value problem |
| topic | Hybrid implicit equations Tempered (κ, ϖ)-hilfer fractional operators Mittag-leffler-ulam-hyers stability Generalized gronwall inequality |
| url | http://www.sciencedirect.com/science/article/pii/S1110016825000973 |
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