Well-posedness and Ulam-Hyers stability results of solutions to pantograph fractional stochastic differential equations in the sense of conformable derivatives
One kind of stochastic delay differential equation in which the delay term is dependent on a proportion of the current time is the pantograph stochastic differential equation. Electric current collection, nonlinear dynamics, quantum mechanics, and electrodynamics are among the phenomena modeled usin...
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AIMS Press
2024-03-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2024605?viewType=HTML |
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| author | Wedad Albalawi Muhammad Imran Liaqat Fahim Ud Din Kottakkaran Sooppy Nisar Abdel-Haleem Abdel-Aty |
| author_facet | Wedad Albalawi Muhammad Imran Liaqat Fahim Ud Din Kottakkaran Sooppy Nisar Abdel-Haleem Abdel-Aty |
| author_sort | Wedad Albalawi |
| collection | DOAJ |
| description | One kind of stochastic delay differential equation in which the delay term is dependent on a proportion of the current time is the pantograph stochastic differential equation. Electric current collection, nonlinear dynamics, quantum mechanics, and electrodynamics are among the phenomena modeled using this equation. A key idea in physics and mathematics is the well-posedness of a differential equation, which guarantees that the solution to the problem exists and is a unique and meaningful solution that relies continuously on the initial condition and the value of the fractional derivative. Ulam-Hyers stability is a property of equations that states that if a function is approximately satisfying the equation, then there exists an exact solution that is close to the function. Inspired by these findings, in this research work, we established the Ulam-Hyers stability and well-posedness of solutions of pantograph fractional stochastic differential equations (PFSDEs) in the framework of conformable derivatives. In addition, we provided examples to analyze the theoretical results. |
| first_indexed | 2024-04-24T09:00:31Z |
| format | Article |
| id | doaj.art-36197e2376424b1ab13d166f4ac08c7b |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-24T09:00:31Z |
| publishDate | 2024-03-01 |
| publisher | AIMS Press |
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| series | AIMS Mathematics |
| spelling | doaj.art-36197e2376424b1ab13d166f4ac08c7b2024-04-16T01:18:31ZengAIMS PressAIMS Mathematics2473-69882024-03-0195123751239810.3934/math.2024605Well-posedness and Ulam-Hyers stability results of solutions to pantograph fractional stochastic differential equations in the sense of conformable derivativesWedad Albalawi0Muhammad Imran Liaqat 1Fahim Ud Din2Kottakkaran Sooppy Nisar3Abdel-Haleem Abdel-Aty41. Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia2. Abdus Salam School of Mathematical Sciences, Government College University, 68-B, New Muslim Town, Lahore 54600, Pakistan2. Abdus Salam School of Mathematical Sciences, Government College University, 68-B, New Muslim Town, Lahore 54600, Pakistan3. Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam bin Abdulaziz University, Alkharj 11942, Saudi Arabia4. Department of Physics, College of Sciences, University of Bisha, Bisha 61922, Saudi ArabiaOne kind of stochastic delay differential equation in which the delay term is dependent on a proportion of the current time is the pantograph stochastic differential equation. Electric current collection, nonlinear dynamics, quantum mechanics, and electrodynamics are among the phenomena modeled using this equation. A key idea in physics and mathematics is the well-posedness of a differential equation, which guarantees that the solution to the problem exists and is a unique and meaningful solution that relies continuously on the initial condition and the value of the fractional derivative. Ulam-Hyers stability is a property of equations that states that if a function is approximately satisfying the equation, then there exists an exact solution that is close to the function. Inspired by these findings, in this research work, we established the Ulam-Hyers stability and well-posedness of solutions of pantograph fractional stochastic differential equations (PFSDEs) in the framework of conformable derivatives. In addition, we provided examples to analyze the theoretical results.https://www.aimspress.com/article/doi/10.3934/math.2024605?viewType=HTMLconformable fractional derivativepantograph fractional stochastic differential equationswell-posednessulam-hyers stability |
| spellingShingle | Wedad Albalawi Muhammad Imran Liaqat Fahim Ud Din Kottakkaran Sooppy Nisar Abdel-Haleem Abdel-Aty Well-posedness and Ulam-Hyers stability results of solutions to pantograph fractional stochastic differential equations in the sense of conformable derivatives AIMS Mathematics conformable fractional derivative pantograph fractional stochastic differential equations well-posedness ulam-hyers stability |
| title | Well-posedness and Ulam-Hyers stability results of solutions to pantograph fractional stochastic differential equations in the sense of conformable derivatives |
| title_full | Well-posedness and Ulam-Hyers stability results of solutions to pantograph fractional stochastic differential equations in the sense of conformable derivatives |
| title_fullStr | Well-posedness and Ulam-Hyers stability results of solutions to pantograph fractional stochastic differential equations in the sense of conformable derivatives |
| title_full_unstemmed | Well-posedness and Ulam-Hyers stability results of solutions to pantograph fractional stochastic differential equations in the sense of conformable derivatives |
| title_short | Well-posedness and Ulam-Hyers stability results of solutions to pantograph fractional stochastic differential equations in the sense of conformable derivatives |
| title_sort | well posedness and ulam hyers stability results of solutions to pantograph fractional stochastic differential equations in the sense of conformable derivatives |
| topic | conformable fractional derivative pantograph fractional stochastic differential equations well-posedness ulam-hyers stability |
| url | https://www.aimspress.com/article/doi/10.3934/math.2024605?viewType=HTML |
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