Stabilization by feedback control of a novel stochastic chaotic finance model with time-varying fractional derivatives
Chaotic systems exhibit a random behavior that may result in undesired system performance. In this context, diverse strategies have been proposed to control the chaos that appears in various areas of applications. Most of them presented in the deterministic case without taking the environmental nois...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-01-01
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| Series: | Alexandria Engineering Journal |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016824012390 |
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| author | Seyfeddine Moualkia Yang Liu Jinde Cao |
| author_facet | Seyfeddine Moualkia Yang Liu Jinde Cao |
| author_sort | Seyfeddine Moualkia |
| collection | DOAJ |
| description | Chaotic systems exhibit a random behavior that may result in undesired system performance. In this context, diverse strategies have been proposed to control the chaos that appears in various areas of applications. Most of them presented in the deterministic case without taking the environmental noises into account, although many systems in practice are often-times exposed to some external disturbances that affect the structure of the considered system. The key aim in this article is to stabilize a chaotic finance model (CFM) by designing feedback controllers in the stochastic and fractional cases. Firstly, we establish a novel set of suitable hypotheses to demonstrate the uniqueness of solutions. Secondly, we discuss the Hyers–Ulam stability (HUS) and the generalized HUS for the controlled CFM under sufficient conditions. Finally, we provide several examples attached with numerical findings which clearly support the validity of theoretical findings and highlight their benefits. The numerical simulations are done based on the Euler–Maruyama method and with the help of Lagrange polynomial interpolation, enabling the authors to extract meaningful results from the model. Compared to the existing CFMs, the present study proposes a novel type of nonlinear controller for the stabilization of the fractional stochastic CFM, providing a substantial analysis based on the HUS theory and computer simulation results to verify the rapid convergence of the state variables to the origin. |
| format | Article |
| id | doaj-art-25b118ad054e4db98840e3eac07d29f0 |
| institution | Kabale University |
| issn | 1110-0168 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj-art-25b118ad054e4db98840e3eac07d29f02025-01-29T05:00:06ZengElsevierAlexandria Engineering Journal1110-01682025-01-01112496509Stabilization by feedback control of a novel stochastic chaotic finance model with time-varying fractional derivativesSeyfeddine Moualkia0Yang Liu1Jinde Cao2School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, China; Department of Mathematics, University of 8 Mai 1945, Guelma 24000, AlgeriaSchool of Mathematics and Statistics, Yili Normal University, Yining, 835000, China; School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, China; Corresponding author at: School of Mathematics and Statistics, Yili Normal University, Yining, 835000, China.School of Mathematics, Southeast University, Nanjing 210096, China; Ahlia University, Manama 10878, BahrainChaotic systems exhibit a random behavior that may result in undesired system performance. In this context, diverse strategies have been proposed to control the chaos that appears in various areas of applications. Most of them presented in the deterministic case without taking the environmental noises into account, although many systems in practice are often-times exposed to some external disturbances that affect the structure of the considered system. The key aim in this article is to stabilize a chaotic finance model (CFM) by designing feedback controllers in the stochastic and fractional cases. Firstly, we establish a novel set of suitable hypotheses to demonstrate the uniqueness of solutions. Secondly, we discuss the Hyers–Ulam stability (HUS) and the generalized HUS for the controlled CFM under sufficient conditions. Finally, we provide several examples attached with numerical findings which clearly support the validity of theoretical findings and highlight their benefits. The numerical simulations are done based on the Euler–Maruyama method and with the help of Lagrange polynomial interpolation, enabling the authors to extract meaningful results from the model. Compared to the existing CFMs, the present study proposes a novel type of nonlinear controller for the stabilization of the fractional stochastic CFM, providing a substantial analysis based on the HUS theory and computer simulation results to verify the rapid convergence of the state variables to the origin.http://www.sciencedirect.com/science/article/pii/S1110016824012390Stochastic chaotic finance modelTime-varying fractional orderFeedback controlHyers–Ulam stability |
| spellingShingle | Seyfeddine Moualkia Yang Liu Jinde Cao Stabilization by feedback control of a novel stochastic chaotic finance model with time-varying fractional derivatives Alexandria Engineering Journal Stochastic chaotic finance model Time-varying fractional order Feedback control Hyers–Ulam stability |
| title | Stabilization by feedback control of a novel stochastic chaotic finance model with time-varying fractional derivatives |
| title_full | Stabilization by feedback control of a novel stochastic chaotic finance model with time-varying fractional derivatives |
| title_fullStr | Stabilization by feedback control of a novel stochastic chaotic finance model with time-varying fractional derivatives |
| title_full_unstemmed | Stabilization by feedback control of a novel stochastic chaotic finance model with time-varying fractional derivatives |
| title_short | Stabilization by feedback control of a novel stochastic chaotic finance model with time-varying fractional derivatives |
| title_sort | stabilization by feedback control of a novel stochastic chaotic finance model with time varying fractional derivatives |
| topic | Stochastic chaotic finance model Time-varying fractional order Feedback control Hyers–Ulam stability |
| url | http://www.sciencedirect.com/science/article/pii/S1110016824012390 |
| work_keys_str_mv | AT seyfeddinemoualkia stabilizationbyfeedbackcontrolofanovelstochasticchaoticfinancemodelwithtimevaryingfractionalderivatives AT yangliu stabilizationbyfeedbackcontrolofanovelstochasticchaoticfinancemodelwithtimevaryingfractionalderivatives AT jindecao stabilizationbyfeedbackcontrolofanovelstochasticchaoticfinancemodelwithtimevaryingfractionalderivatives |