THE SIGNIFICANCE OF OPTIMAL ALGORITHMS FOR FRACTIONAL-ORDER DIFFERENTIAL EQUATIONS IN MODELING DYNAMIC PROCESSES IN THE FINANCIAL MARKET

Murodulla Boboqulov

doi:10.60078/2026-vol5-iss3-pp391-392

Mualliflar

Murodulla Boboqulov

Tashkent branch of Samarkand State University of Veterinary Medicine

DOI:

https://doi.org/10.60078/2026-vol5-iss3-pp391-392

Annotasiya

Modern financial markets exhibit complex, non-linear behaviors that classical integer-order models often fail to capture adequately. The application of fractional- order differential equations (FODEs) has emerged as a superior mathematical framework due to its inherent ability to model "memory effects" and long-range dependencies in asset price fluctuations. This research focuses on the critical role of optimal algorithms in solving these equations to enhance the predictive accuracy of financial models.

Bibliografik manbalar

1. Podlubny, I. (1999). Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications. Academic Press. (Kasr tartibli hisoblash bo'yicha fundamental asar).

2. Mainardi, F. (2010). Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models. Imperial College Press.

3. Hayotov, A. R., & Rasulov, M. (2021). Optimal Quadrature Formulas for Fractional Integrals and Their Applications in Numerical Analysis. Journal of Computational Mathematics. (Optimal algoritmlar bo'yicha muhim tadqiqot).

4. Tarasov, V. E. (2011). Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media. Springer Science & Business Media.

5. Kilbas, A. A., Srivastava, H. M., & Trujillo, J. J. (2006). Theory and Applications of Fractional Differential Equations. Elsevier.

6. Baleanu, D., Guvenc, Z. B., & Machado, J. T. (2011). New Trends in Nanotechnology and Fractional Calculus Applications. Springer.

7. Scaling and Fractional Derivatives in Game Theory and Financial Mathematics. (2015). In Fractional Dynamics (pp. 357-378). (Moliya va o'yinlar nazariyasi kesishmasidagi tadqiqot).

8. Sun, H. G., Zhang, Y., Baleanu, D., Chen, W., & Chen, Y. Q. (2018). A new look at the fractional calculus: From the mathematical model to applications in physics and engineering. Communications in Nonlinear Science and Numerical Simulation.

9. West, B. J. (2016). Fractional Calculus View of Complexity: Tomorrow’s Science. CRC Press.

10. He, J. H. (1999). Variational iteration method – a kind of non-linear analytical technique: some examples. International Journal of Non-Linear Mechanics. (Sonli usullar uchun muhim manba).