Analysis of Noise on Ordinary and Fractional-Order Financial Systems
This study investigated the influence of stochastic fluctuations on financial system stability by analyzing both ordinary and fractional-order financial models under noise. The ordinary financial system experiences perturbations due to bounded random disturbances, whereas the fractional-order counte...
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MDPI AG
2025-05-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/9/5/316 |
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| author | Hunida Malaikah Jawaher Faisal Alabdali |
| author_facet | Hunida Malaikah Jawaher Faisal Alabdali |
| author_sort | Hunida Malaikah |
| collection | DOAJ |
| description | This study investigated the influence of stochastic fluctuations on financial system stability by analyzing both ordinary and fractional-order financial models under noise. The ordinary financial system experiences perturbations due to bounded random disturbances, whereas the fractional-order counterpart models memory-dependent behaviors by incorporating fractional Gaussian noise (FGN) characterized by a Hurst parameter that governs long-term correlations. This study used data generated through MATLAB simulations based on standard financial models from the literature. Numerical simulations compared system behavior in deterministic and noisy environments. The results reveal that ordinary systems experience transient fluctuations, quickly returning to a stable state, whereas fractional systems exhibit persistent deviations due to historical dependencies. This highlights the fundamental difference between integer-order and fractional-order derivatives in financial modeling. Our key findings indicate that noise significantly impacts interest rates, investment needs, price indices, and profit margins, with the fractional system displaying higher sensitivity to external shocks. These insights emphasize the necessity of incorporating memory effects in financial modeling to improve accuracy in predicting market behavior. The study further underscores the importance of adaptive monetary policies and risk management strategies to mitigate financial instability. Future research should explore hybrid models combining short-term stability with long-term memory effects for enhanced financial forecasting and stability analysis. |
| format | Article |
| id | doaj-art-14aa1addfb384007bd5f8aa0f448ebdc |
| institution | OA Journals |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-14aa1addfb384007bd5f8aa0f448ebdc2025-08-20T01:56:24ZengMDPI AGFractal and Fractional2504-31102025-05-019531610.3390/fractalfract9050316Analysis of Noise on Ordinary and Fractional-Order Financial SystemsHunida Malaikah0Jawaher Faisal Alabdali1Mathematics Department, King Abdulaziz University, Jeddah 21589, Saudi ArabiaMathematics Department, King Abdulaziz University, Jeddah 21589, Saudi ArabiaThis study investigated the influence of stochastic fluctuations on financial system stability by analyzing both ordinary and fractional-order financial models under noise. The ordinary financial system experiences perturbations due to bounded random disturbances, whereas the fractional-order counterpart models memory-dependent behaviors by incorporating fractional Gaussian noise (FGN) characterized by a Hurst parameter that governs long-term correlations. This study used data generated through MATLAB simulations based on standard financial models from the literature. Numerical simulations compared system behavior in deterministic and noisy environments. The results reveal that ordinary systems experience transient fluctuations, quickly returning to a stable state, whereas fractional systems exhibit persistent deviations due to historical dependencies. This highlights the fundamental difference between integer-order and fractional-order derivatives in financial modeling. Our key findings indicate that noise significantly impacts interest rates, investment needs, price indices, and profit margins, with the fractional system displaying higher sensitivity to external shocks. These insights emphasize the necessity of incorporating memory effects in financial modeling to improve accuracy in predicting market behavior. The study further underscores the importance of adaptive monetary policies and risk management strategies to mitigate financial instability. Future research should explore hybrid models combining short-term stability with long-term memory effects for enhanced financial forecasting and stability analysis.https://www.mdpi.com/2504-3110/9/5/316financial systemsnoisefractional Gaussian noisesystem stabilityeconomic modelingexternal shocks |
| spellingShingle | Hunida Malaikah Jawaher Faisal Alabdali Analysis of Noise on Ordinary and Fractional-Order Financial Systems Fractal and Fractional financial systems noise fractional Gaussian noise system stability economic modeling external shocks |
| title | Analysis of Noise on Ordinary and Fractional-Order Financial Systems |
| title_full | Analysis of Noise on Ordinary and Fractional-Order Financial Systems |
| title_fullStr | Analysis of Noise on Ordinary and Fractional-Order Financial Systems |
| title_full_unstemmed | Analysis of Noise on Ordinary and Fractional-Order Financial Systems |
| title_short | Analysis of Noise on Ordinary and Fractional-Order Financial Systems |
| title_sort | analysis of noise on ordinary and fractional order financial systems |
| topic | financial systems noise fractional Gaussian noise system stability economic modeling external shocks |
| url | https://www.mdpi.com/2504-3110/9/5/316 |
| work_keys_str_mv | AT hunidamalaikah analysisofnoiseonordinaryandfractionalorderfinancialsystems AT jawaherfaisalalabdali analysisofnoiseonordinaryandfractionalorderfinancialsystems |