Analysis of fractal fractional Lorenz type and financial chaotic systems with exponential decay kernels
In this work, we formulate a fractal fractional chaotic system with cubic and quadratic nonlinearities. A fractal fractional chaotic Lorenz type and financial systems are studied using the Caputo Fabrizo (CF) fractal fractional derivative. This study focuses on the characterization of the chaotic na...
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-08-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20221035?viewType=HTML |
| _version_ | 1811188112636772352 |
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| author | Ihtisham Ul Haq Shabir Ahmad Sayed Saifullah Kamsing Nonlaopon Ali Akgül |
| author_facet | Ihtisham Ul Haq Shabir Ahmad Sayed Saifullah Kamsing Nonlaopon Ali Akgül |
| author_sort | Ihtisham Ul Haq |
| collection | DOAJ |
| description | In this work, we formulate a fractal fractional chaotic system with cubic and quadratic nonlinearities. A fractal fractional chaotic Lorenz type and financial systems are studied using the Caputo Fabrizo (CF) fractal fractional derivative. This study focuses on the characterization of the chaotic nature, and the effects of the fractal fractional-order derivative in the CF sense on the evolution and behavior of each proposed systems. The stability of the equilibrium points for the both systems are investigated using the Routh-Hurwitz criterion. The numerical scheme, which includes the discretization of the CF fractal-fractional derivative, is used to depict the phase portraits of the fractal fractional chaotic Lorenz system and the fractal fractional-order financial system. The simulation results presented in both cases include the two- and three-dimensional phase portraits to evaluate the applications of the proposed operators. |
| first_indexed | 2024-04-11T14:15:00Z |
| format | Article |
| id | doaj.art-c1f6a468e2b841079c8c1f53bbeeafc2 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-11T14:15:00Z |
| publishDate | 2022-08-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-c1f6a468e2b841079c8c1f53bbeeafc22022-12-22T04:19:35ZengAIMS PressAIMS Mathematics2473-69882022-08-01710188091882310.3934/math.20221035Analysis of fractal fractional Lorenz type and financial chaotic systems with exponential decay kernelsIhtisham Ul Haq 0Shabir Ahmad1Sayed Saifullah2Kamsing Nonlaopon3Ali Akgül 41. Department of Mathematics, University of Malakand, Chakdara, Dir Lower, Khyber Pakhtunkhwa, Pakistan1. Department of Mathematics, University of Malakand, Chakdara, Dir Lower, Khyber Pakhtunkhwa, Pakistan1. Department of Mathematics, University of Malakand, Chakdara, Dir Lower, Khyber Pakhtunkhwa, Pakistan2. Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand3. Siirt University, Art and Science Faculty, Department of Mathematics, TR-56100 Siirt, TurkeyIn this work, we formulate a fractal fractional chaotic system with cubic and quadratic nonlinearities. A fractal fractional chaotic Lorenz type and financial systems are studied using the Caputo Fabrizo (CF) fractal fractional derivative. This study focuses on the characterization of the chaotic nature, and the effects of the fractal fractional-order derivative in the CF sense on the evolution and behavior of each proposed systems. The stability of the equilibrium points for the both systems are investigated using the Routh-Hurwitz criterion. The numerical scheme, which includes the discretization of the CF fractal-fractional derivative, is used to depict the phase portraits of the fractal fractional chaotic Lorenz system and the fractal fractional-order financial system. The simulation results presented in both cases include the two- and three-dimensional phase portraits to evaluate the applications of the proposed operators.https://www.aimspress.com/article/doi/10.3934/math.20221035?viewType=HTMLfractal fractional calculuschaotic lorenz systemfinancial systemrouth-hurwitz stability criterion |
| spellingShingle | Ihtisham Ul Haq Shabir Ahmad Sayed Saifullah Kamsing Nonlaopon Ali Akgül Analysis of fractal fractional Lorenz type and financial chaotic systems with exponential decay kernels AIMS Mathematics fractal fractional calculus chaotic lorenz system financial system routh-hurwitz stability criterion |
| title | Analysis of fractal fractional Lorenz type and financial chaotic systems with exponential decay kernels |
| title_full | Analysis of fractal fractional Lorenz type and financial chaotic systems with exponential decay kernels |
| title_fullStr | Analysis of fractal fractional Lorenz type and financial chaotic systems with exponential decay kernels |
| title_full_unstemmed | Analysis of fractal fractional Lorenz type and financial chaotic systems with exponential decay kernels |
| title_short | Analysis of fractal fractional Lorenz type and financial chaotic systems with exponential decay kernels |
| title_sort | analysis of fractal fractional lorenz type and financial chaotic systems with exponential decay kernels |
| topic | fractal fractional calculus chaotic lorenz system financial system routh-hurwitz stability criterion |
| url | https://www.aimspress.com/article/doi/10.3934/math.20221035?viewType=HTML |
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