New Results on the Stability and Existence of Langevin Fractional Differential Equations with Boundary Conditions
This manuscript aims to establish the existence, uniqueness, and stability of solutions for Langevin fractional differential equations involving the generalized Liouville-Caputo derivative. Using a novel approach, we derive existence and uniqueness results through fixed-point theorems, extending and...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-02-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/9/2/127 |
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| _version_ | 1849719186163499008 |
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| author | Rahman Ullah Khan Maria Samreen Gohar Ali Ioan-Lucian Popa |
| author_facet | Rahman Ullah Khan Maria Samreen Gohar Ali Ioan-Lucian Popa |
| author_sort | Rahman Ullah Khan |
| collection | DOAJ |
| description | This manuscript aims to establish the existence, uniqueness, and stability of solutions for Langevin fractional differential equations involving the generalized Liouville-Caputo derivative. Using a novel approach, we derive existence and uniqueness results through fixed-point theorems, extending and generalizing several existing findings in the literature. To demonstrate the applicability of our results, we provide a practical example that validates the theoretical framework. |
| format | Article |
| id | doaj-art-28c8a15c82bc4087a8840d33f84b5384 |
| institution | DOAJ |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-28c8a15c82bc4087a8840d33f84b53842025-08-20T03:12:11ZengMDPI AGFractal and Fractional2504-31102025-02-019212710.3390/fractalfract9020127New Results on the Stability and Existence of Langevin Fractional Differential Equations with Boundary ConditionsRahman Ullah Khan0Maria Samreen1Gohar Ali2Ioan-Lucian Popa3Department of Mathematics, Quaid-i-Azam University, Islamabad 45320, PakistanDepartment of Mathematics, Quaid-i-Azam University, Islamabad 45320, PakistanDepartment of Mathematics, Islamia College Peshawar, Peshawar 25120, Khyber Pakhtunkhwa, PakistanDepartment of Computing, Mathematics and Electronics, 1 Decembrie 1918 University of Alba Iulia, 510009 Alba Iulia, RomaniaThis manuscript aims to establish the existence, uniqueness, and stability of solutions for Langevin fractional differential equations involving the generalized Liouville-Caputo derivative. Using a novel approach, we derive existence and uniqueness results through fixed-point theorems, extending and generalizing several existing findings in the literature. To demonstrate the applicability of our results, we provide a practical example that validates the theoretical framework.https://www.mdpi.com/2504-3110/9/2/127Langevin fractional differential equationsgeneralized Liouville–Caputo derivativefixed point resultsstability |
| spellingShingle | Rahman Ullah Khan Maria Samreen Gohar Ali Ioan-Lucian Popa New Results on the Stability and Existence of Langevin Fractional Differential Equations with Boundary Conditions Fractal and Fractional Langevin fractional differential equations generalized Liouville–Caputo derivative fixed point results stability |
| title | New Results on the Stability and Existence of Langevin Fractional Differential Equations with Boundary Conditions |
| title_full | New Results on the Stability and Existence of Langevin Fractional Differential Equations with Boundary Conditions |
| title_fullStr | New Results on the Stability and Existence of Langevin Fractional Differential Equations with Boundary Conditions |
| title_full_unstemmed | New Results on the Stability and Existence of Langevin Fractional Differential Equations with Boundary Conditions |
| title_short | New Results on the Stability and Existence of Langevin Fractional Differential Equations with Boundary Conditions |
| title_sort | new results on the stability and existence of langevin fractional differential equations with boundary conditions |
| topic | Langevin fractional differential equations generalized Liouville–Caputo derivative fixed point results stability |
| url | https://www.mdpi.com/2504-3110/9/2/127 |
| work_keys_str_mv | AT rahmanullahkhan newresultsonthestabilityandexistenceoflangevinfractionaldifferentialequationswithboundaryconditions AT mariasamreen newresultsonthestabilityandexistenceoflangevinfractionaldifferentialequationswithboundaryconditions AT goharali newresultsonthestabilityandexistenceoflangevinfractionaldifferentialequationswithboundaryconditions AT ioanlucianpopa newresultsonthestabilityandexistenceoflangevinfractionaldifferentialequationswithboundaryconditions |