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Fuzzy approximation of a fractional Lorenz system and a fractional financial crisis | ||
| Iranian Journal of Fuzzy Systems | ||
| دوره 20، شماره 7، بهمن و اسفند 2023، صفحه 27-36 اصل مقاله (197.9 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2023.7628 | ||
| نویسندگان | ||
| S. Rezaei Aderyani1؛ R. Saadati2؛ T. Allahviranloo3؛ S. Abbasbandy* 4؛ M. Catak5 | ||
| 1School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran | ||
| 2Department of Mathematics, Iran University of Science and Technology, Tehran, Iran | ||
| 3Faculty of engineering and natural science, Istinye university, Istanbul, Turkey. | ||
| 4Department of Applied Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran | ||
| 5College of Engineering and Technology, American University of the Middle East, Kuwait | ||
| چکیده | ||
| Our aim in this paper is to study the fuzzy stability of a fractional Lorenz system in the sense of the Caputo-Fabrizio derivative and a fractional financial crisis in the sense of }−Hilfer derivative. Defining a new type of fuzzy control function that has a dynamic situation helps us to investigate new stability results for these mathematical models. | ||
| کلیدواژه‌ها | ||
| Fractional Lorenz system؛ stability؛ Caputo-Fabrizio derivative؛ fractional financial crisis؛ fuzzy sets | ||
| مراجع | ||
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[2] A. Atangana, Fractal-fractional differentiation and integration: Connecting fractal calculus and fractional calculus to predict complex system, Chaos Solitons Fractals, 102 (2017), 396-406.
[3] B. W. Fang, J. K. Wu, On interval fuzzy implications derived from interval additive generators of interval t-norms, International Journal of Approximate Reasoning, 153 (2023), 1-17.
[4] S. Guo, A. C. Luo, To infinitely many spiral homoclinic orbits from periodic motions in the Lorenz system, International Journal of Dynamics and Control, 11(1) (2023), 17-65.
[5] A. Korobeinikov, Financial crisis: An attempt of mathematical modelling, Applied Mathematics Letters, 22(12) (2009), 1882-1886.
[6] M. Liu, L. Chen, X. B. Shu, The existence of positive solutions for phi-Hilfer fractional differential equation with random impulses and boundary value conditions, Waves in Random and Complex Media, (2023), 1-19.
[7] S. Rezaei Aderyani, R. Saadati, Best approximations of the ϕ-Hadamard fractional Volterra integro-differential equation by matrix valued fuzzy control functions, Advances in Difference Equations, 154 (2021), 21. DOI:10.1186/s 13662-021-03305-z.
[8] S. Rezaei Aderyani, R. Saadati, X. J. Yang, Radu-Mihet method for UHML stability for a class of ξ-Hilfer fractional differential equations in matrix valued fuzzy Banach spaces, Mathematical Methods in the Applied Sciences, 44(18) (2021), 14619-14631.
[9] Y. Su, R. Mesiar, Representation and construction of homogeneous and quasi-homogeneous n-ary aggregation functions, Kybernetika (Prague), 57(6) (2021), 958-969.
[10] Y. Su, W. Zong, R. Mesiar, Characterization of homogeneous and quasi-homogeneous binary aggregation functions, Fuzzy Sets and Systems, 433 (2022), 96-107.
[11] S. Thalabard, J. Bec, A. A. Mailybaev, From the butterfly effect to spontaneous stochasticity in singular shear flows, Communications Physics, Nature Publishing Group, 2020.
[12] S. Ucar, Analysis of hepatitis B disease with fractal–fractional Caputo derivative using real data from Turkey, Journal of Computational and Applied Mathematics, 419 (2023), 114692. | ||
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