Document Details
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Document Type |
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Thesis |
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Document Title |
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BOUNDARY VALUE PROBLEMS FOR FRACTIONAL LANGEVIN EQUATIONS مسائل القيم الحدية لمعادلات لانجفن الكسرية |
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Subject |
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Faculty of Science |
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Document Language |
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Arabic |
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Abstract |
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Boundary value problems for fractional Langevin equations By Lamyaa Ayed Almughamisi A thesis submitted for the requirements of the degree of PhD in Mathematics-Differential Equations Supervised By Prof. Dr. Ahmed Salem El-Sherif and Dr. Faris S. Alzahrani This thesis studies some new boundary value problems of Langevin fractional differential equations, Sturm-Liouville and Langevin fractional equation in generalized framework and coupled fractional-order systems supplemented with Riemann-Stieltjes and some other kinds of nonlocal boundary conditions. As a firs problem, we introduce a class of nonlinear Langevin equation involving two fractional orders with nonlocal integral and three-point boundary conditions. In the second problem, we investigate a class of nonlinear Langevin equation involving one fractional order with three-point boundary conditions. The third problem deals with some existence results of solutions for Langevin equations including two distinct fractional orders subject to nonlocal boundary conditions, by using coupled fixed point theorems as a main tool to prove our essential results for mixed monotone property which is applied in a partially ordered set (POSET). In the fourth problem, by using Shauder fixed-point theorem, we obtain the results for the existence of solution for a coupled system of Langevin fractional differential equations of Caputo type subject to Stieltjes integral boundary conditions. The last problem, we combine Sturm-Liouville and Langevin fractional differential equations in order to introduce a new class of nonlocal integral boundary value problems with generalized fractional derivative type. The results presented in this thesis have been published or accepted for publication in SCI journals. |
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Supervisor |
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Prof. Dr. Ahmed Salem Al-Sherif |
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Thesis Type |
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Doctorate Thesis |
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Publishing Year |
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1443 AH
2022 AD |
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Co-Supervisor |
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Dr. Faris S. Alzahrani |
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Added Date |
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Sunday, March 6, 2022 |
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Researchers
| لمياء عايد المغامسي | Almughamisi, Lamyaa Ayed | Researcher | Doctorate | |
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