Stochastic Optimal Control Analysis of a Mathematical Model: Theory and Application to Non-Singular Kernels
Some researchers believe fractional differential operators should not have a non-singular kernel, while others strongly believe that due to the complexity of nature, fractional differential operators can have either singular or non-singular kernels. This contradiction in thoughts has led to the publ...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-05-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/6/5/279 |
| _version_ | 1797499760444178432 |
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| author | Anwarud Din Qura Tul Ain |
| author_facet | Anwarud Din Qura Tul Ain |
| author_sort | Anwarud Din |
| collection | DOAJ |
| description | Some researchers believe fractional differential operators should not have a non-singular kernel, while others strongly believe that due to the complexity of nature, fractional differential operators can have either singular or non-singular kernels. This contradiction in thoughts has led to the publication of a few papers that are against differential operators with non-singular kernels, causing some negative impacts. Thus, publishers and some Editors-in-Chief are concerned about the future of fractional calculus, which has generally brought confusion among the vibrant and innovative young researchers who desire to apply fractional calculus within their respective fields. Thus, the present work aims to develop a model based on a stochastic process that could be utilized to portray the effect of arbitrary-order derivatives. A nonlinear perturbation is used to study the proposed stochastic model with the help of white noises. The required condition(s) for the existence of an ergodic stationary distribution is obtained via Lyapunov functional theory. The finding of the study indicated that the proposed noises have a remarkable impact on the dynamics of the system. To reduce the spread of a disease, we imposed some control measures on the stochastic model, and the optimal system was achieved. The models both with and without control were coded in MATLAB, and at the conclusion of the research, numerical solutions are provided. |
| first_indexed | 2024-03-10T03:52:03Z |
| format | Article |
| id | doaj.art-3d988b4efd7d4e2e869aac1ad3ba90f6 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T03:52:03Z |
| publishDate | 2022-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-3d988b4efd7d4e2e869aac1ad3ba90f62023-11-23T11:03:56ZengMDPI AGFractal and Fractional2504-31102022-05-016527910.3390/fractalfract6050279Stochastic Optimal Control Analysis of a Mathematical Model: Theory and Application to Non-Singular KernelsAnwarud Din0Qura Tul Ain1Department of Mathematics, Sun Yat-Sen University, Guangzhou 510275, ChinaDepartment of Mathematics, Guizhou University, Guiyang 550025, ChinaSome researchers believe fractional differential operators should not have a non-singular kernel, while others strongly believe that due to the complexity of nature, fractional differential operators can have either singular or non-singular kernels. This contradiction in thoughts has led to the publication of a few papers that are against differential operators with non-singular kernels, causing some negative impacts. Thus, publishers and some Editors-in-Chief are concerned about the future of fractional calculus, which has generally brought confusion among the vibrant and innovative young researchers who desire to apply fractional calculus within their respective fields. Thus, the present work aims to develop a model based on a stochastic process that could be utilized to portray the effect of arbitrary-order derivatives. A nonlinear perturbation is used to study the proposed stochastic model with the help of white noises. The required condition(s) for the existence of an ergodic stationary distribution is obtained via Lyapunov functional theory. The finding of the study indicated that the proposed noises have a remarkable impact on the dynamics of the system. To reduce the spread of a disease, we imposed some control measures on the stochastic model, and the optimal system was achieved. The models both with and without control were coded in MATLAB, and at the conclusion of the research, numerical solutions are provided.https://www.mdpi.com/2504-3110/6/5/279stochastic model of the survival of fractional calculusnonlinear perturbationstationary distributionstochastic optimality |
| spellingShingle | Anwarud Din Qura Tul Ain Stochastic Optimal Control Analysis of a Mathematical Model: Theory and Application to Non-Singular Kernels Fractal and Fractional stochastic model of the survival of fractional calculus nonlinear perturbation stationary distribution stochastic optimality |
| title | Stochastic Optimal Control Analysis of a Mathematical Model: Theory and Application to Non-Singular Kernels |
| title_full | Stochastic Optimal Control Analysis of a Mathematical Model: Theory and Application to Non-Singular Kernels |
| title_fullStr | Stochastic Optimal Control Analysis of a Mathematical Model: Theory and Application to Non-Singular Kernels |
| title_full_unstemmed | Stochastic Optimal Control Analysis of a Mathematical Model: Theory and Application to Non-Singular Kernels |
| title_short | Stochastic Optimal Control Analysis of a Mathematical Model: Theory and Application to Non-Singular Kernels |
| title_sort | stochastic optimal control analysis of a mathematical model theory and application to non singular kernels |
| topic | stochastic model of the survival of fractional calculus nonlinear perturbation stationary distribution stochastic optimality |
| url | https://www.mdpi.com/2504-3110/6/5/279 |
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