The Sequential Conformable Langevin-Type Differential Equations and Their Applications to the RLC Electric Circuit Problems
In this paper, the sequential conformable Langevin-type differential equation is studied. A representation of a solution consisting of the newly defined conformable bivariate Mittag-Leffler function to its nonhomogeneous and linear version is obtained via the conformable Laplace transforms’ techniqu...
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2024/3680383 |
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| author | M. Aydin N. I. Mahmudov |
| author_facet | M. Aydin N. I. Mahmudov |
| author_sort | M. Aydin |
| collection | DOAJ |
| description | In this paper, the sequential conformable Langevin-type differential equation is studied. A representation of a solution consisting of the newly defined conformable bivariate Mittag-Leffler function to its nonhomogeneous and linear version is obtained via the conformable Laplace transforms’ technique. Also, existence and uniqueness of a global solution to its nonlinear version are obtained. The existence and uniqueness of solutions are shown with respect to the weighted norm defined in compliance with (conformable) exponential function. The concept of the Ulam–Hyers stability of solutions is debated based on the fixed-point approach. The LRC electrical circuits are presented as an application to the described system. Simulated and numerical instances are offered to instantiate our abstract findings. |
| format | Article |
| id | doaj-art-215a50a4759c47fca118e0a63cf3b7ef |
| institution | OA Journals |
| issn | 1687-0042 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-215a50a4759c47fca118e0a63cf3b7ef2025-08-20T02:03:57ZengWileyJournal of Applied Mathematics1687-00422024-01-01202410.1155/2024/3680383The Sequential Conformable Langevin-Type Differential Equations and Their Applications to the RLC Electric Circuit ProblemsM. Aydin0N. I. Mahmudov1Department of Medical Services and TechniquesDepartment of MathematicsIn this paper, the sequential conformable Langevin-type differential equation is studied. A representation of a solution consisting of the newly defined conformable bivariate Mittag-Leffler function to its nonhomogeneous and linear version is obtained via the conformable Laplace transforms’ technique. Also, existence and uniqueness of a global solution to its nonlinear version are obtained. The existence and uniqueness of solutions are shown with respect to the weighted norm defined in compliance with (conformable) exponential function. The concept of the Ulam–Hyers stability of solutions is debated based on the fixed-point approach. The LRC electrical circuits are presented as an application to the described system. Simulated and numerical instances are offered to instantiate our abstract findings.http://dx.doi.org/10.1155/2024/3680383 |
| spellingShingle | M. Aydin N. I. Mahmudov The Sequential Conformable Langevin-Type Differential Equations and Their Applications to the RLC Electric Circuit Problems Journal of Applied Mathematics |
| title | The Sequential Conformable Langevin-Type Differential Equations and Their Applications to the RLC Electric Circuit Problems |
| title_full | The Sequential Conformable Langevin-Type Differential Equations and Their Applications to the RLC Electric Circuit Problems |
| title_fullStr | The Sequential Conformable Langevin-Type Differential Equations and Their Applications to the RLC Electric Circuit Problems |
| title_full_unstemmed | The Sequential Conformable Langevin-Type Differential Equations and Their Applications to the RLC Electric Circuit Problems |
| title_short | The Sequential Conformable Langevin-Type Differential Equations and Their Applications to the RLC Electric Circuit Problems |
| title_sort | sequential conformable langevin type differential equations and their applications to the rlc electric circuit problems |
| url | http://dx.doi.org/10.1155/2024/3680383 |
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