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The generalized solution of fractional di§erential equations sample with Brownian motion | ||
| International Journal of Nonlinear Analysis and Applications | ||
| دوره 15، شماره 1، فروردین 2024، صفحه 361-371 اصل مقاله (426.39 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.29135.4069 | ||
| نویسندگان | ||
| Nabil Laiche* 1؛ Laid Gasmi2؛ Zouaoui Chikr Elmezouar3؛ Ozen Ozer4 | ||
| 1Department of Mathematics, Oum El Bouaghi University, Algeria | ||
| 2Department of Mathematics, Adrar University, Algeria | ||
| 3Department of Mathematics, College of Science King Khalid University, Abha, Saudi Arabia | ||
| 4Department of Mathematics, Kırklareli University, Faculty of Science and Arts, Turkey | ||
| تاریخ دریافت: 07 آذر 1401، تاریخ بازنگری: 05 شهریور 1402، تاریخ پذیرش: 10 شهریور 1402 | ||
| چکیده | ||
| It is well known that the solution of fractional models proved to be a powerful tool in studying various problems which appear in the sciences of real life. In view of the fact that economic applications are accelerating at an amazing pace, and the large number of modeling in this speciality, it has expanded the number of problems. So, our contribution is based on finding generalized solutions of a fractional differential equation known for their applications in microeconomics and finance and creating an algorithm which allows us to estimate the coefficients of this type of equation. And to really illustrate our results we will choose a model known in the stochastic literature by COGARCH but with fractional derivative, to demonstrate the asymptotic behavior of the estimators, including the impact of fractional order on the space of stochastic differential equations. | ||
| کلیدواژهها | ||
| Fractional derivative؛ fractional COGARCH؛ estimators؛ brownian motion | ||
| مراجع | ||
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[1] A. Bibi and A.J. Oyet, Estimation of some bilinear time series models with time varying coefficients, Stochastic Anal. Appl. 22 (2004), no. 2, 355–376. [2] L.C. Evans, An Introduction to Stochastic Differential Equations, American Mathematical Society, 2012. [3] C. Francq and J.M. Zakoian, GARCH Models: Structure, Statistical Inference and Financial Applications, John Wiley & Sons, 2019. [4] S. Haug, C. Kluppelberg, A. Lindner, and M. Zapp, Method of moment estimation in the COGARCH (1, 1) model, Economet. J. 10 (2007), no. 2, 320–341. [5] R, Hilfer, Applications of Fractional Calculus in Physics, World Scientific, 2000. [6] J. Kallsen and B. Vesenmayer, COGARCH as a continuous-time limit of GARCH (1, 1), Stochastic Process. Appl. 119 (2009), no. 1, 74–98. [7] M.B. Khan, G. Santos-Garc´ıa, M.A. Noor, and M. S. Soliman, Some new concepts related to fuzzy fractional calculus for up and down convex fuzzy-number valued functions and inequalities, Chaos Solitons Fractals 164 (2022), 112692. [8] C. Kluppelberg, R. Maller, and A. Szimayer, The COGARCH: a review, with news on option pricing and statistical inference, Surveys Stochastic Processes, 2011, pp. 29–58. [9] I. Koca and A. Atangana, Some chaotic mathematical models with stochastic resetting, Fractals 30 (2022), no. 8, 2240212. [10] L. Nabil, G. Laid, and Z. Halim, New perspectives in space of COGARCH (1, 1) models with fractional derivative, Turk. J. Comput. Math. Educ. 14 (2023), no. 2, 877–887. [11] I. Podlubny, Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications, Elsevier, 1998. [12] T.S. Rao and M.M. Gabr, An introduction to Bispectral Analysis and Bilinear Time Series Models, Springer Science & Business Media, 2012. [13] E. Scalas, R. Gorenflo, and F. Mainardi, Fractional calculus and continuous-time finance, Phys. A: Statist. Mech. Appl. 284 (2000), no. 1-4, 376–384. [14] J.M. Zakoian, Threshold heteroskedastic models, J. Econ. Dyn. Control 18 (1994), no. 5, 931–955. [15] Z. Zhang and G. Karniadakis, Numerical Methods for Stochastic Partial Differential Equations with White Noise, Berlin, Springer, 2017. [16] Y. Zhou, L. Shangerganesh, J. Manimaran, and A. Debbouche, A class of time-fractional reaction-diffusion equation with nonlocal boundary condition, Math. Meth. Appl. Sci. 41 (2018), no. 8, 2987–2999. [17] Y. Zhou, J.R. Wang, and L. Zhang, Basic Theory of Fractional Differential Equations, World Scientific, 2016. | ||
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