Page 47 - IJOCTA-15-2

M. M. Parsa, K. Sayevand, H. Jafari, I. Masti / IJOCTA, Vol.15, No.2, pp.225-244 (2025)
Availability of data 2023;425:115066.
https://doi.org/10.1016/j.cam.2023.115066
Ph.D. thesis dissertations are public documents, 12. Tajadodi H, Jafari H, Ncube MN. Genocchi poly-
but at the moment are not internet-accessible. If nomials as a tool for solving a class of fractional
one is interested in revising the investigation, in- optimal control problems, An International Jour-
formation can be requested from the authors. nal of Optimization and Control: Theories & Ap-
plications. 2022;12(2):160-168.
https://doi.org/10.11121/ijocta.2022.1263
References
13. Uzun PY, Uzun K, Koca I. The effect of frac-
1. Meerschaert MM, Sikorskii A. Stochastic Models tional order mathematical modelling for exami-
for Fractional Calculus, in: De Gruyter Studies nation of academic achievement in schools with
in Mathematics. De Gruyter: Berlin. 2012;43. stochastic behaviors, An International Journal of
2. Cartea A, del-Castillo-Negrete D. Fractional dif- Optimization and Control: Theories & Applica-
fusion models of option prices in markets with tions. 2023;13(2):244-258.
jumps, Physica A. 2007;2(374):749-763. https://doi.org/10.11121/ijocta.2023.1366
https://doi.org/10.1016/j.physa.2006.08.071 14. Tassaddiq A, Srivastava R, Alharbi R, Kas-
3. Wyss W. The fractional Black-Scholes equa- mani RM, Qureshi S. An application of mul-
tion, Fractional Calculus and Applied Analysis. tiple Erdelyi-Kober fractional integral operators
2000;3(1): 51-61. to establish new inequalities involving a gen-
4. Banihashemi S, Ghasemifard A, Babaei A.On eral class of functions, Fractal and Fractional.
the numerical option pricing methods: fractional 2024;8(8):438.
Black-Scholes equations with CEV assets, Com- https://doi.org/10.3390/fractalfract8080438
putational Economics.2023; 15. Niu H, Chen Y, West BJ. Why do big data and
https://doi.org/10.1007/s10614-023-10482-4 machine learning entail the fractional dynamics?
5. Shahnazi-Pour A, Parsa Moghaddam B, Babaei Entropy. 2021;23(3):297.
A. A computational technique for nonlinear non- https://doi.org/10.3390/e23030297
local stochastic dynamical systems with variable 16. Tassaddiq A, Shabbir MS, Din Q, Naaz H. Dis-
order fractional Brownian noise, Journal of Ap- cretization, bifurcation, and control for a class
plied Nonlinear Dynamics. 2023;12(1):75-85. of predator-prey interactions, Fractal and Frac-
https://doi.org/10.5890/JAND.2023.03.005 tional. 2022;6(1):31.
6. Yoo Y. Stochastic calculus and Black-scholes https://doi.org/10.3390/fractalfract6010031
model, University of Chicago.2017; 17. Tassaddiq A. General escape criteria for the gen-
https://math.uchicago.edu/may/REU2017/ eration of fractals in extended Jungck-Noor or-
REUPapers/Yoo.pdf bit, Mathematics and Computers in Simulation,.
7. Baleanu D, Guvenc ZB, Machado JT. New Trends 2022;196:1-14.
in Nanotechnology and Fractional Calculus Ap- https://doi.org/10.1016/j.matcom.2022.01.003
plications, Springer Science and Business Media, 18. Naik PA, Naveen S, Parthiban V, Qureshi S,
New York. 2010; Alquran M, Senol M. Advancing Lotka-Volterra
https://doi.org/10.1007/978-90-481-3293-5 system simulation with variable fractional order
8. Demirtas M, Ahmad F. Fractional fuzzy PI con- Caputo derivative for enhanced dynamic analy-
troller using particle swarm optimization to im- sis, Journal of Applied Analysis & Computation.
prove power factor by boost converter, An In- 2025;15(2):1002-1019.
ternational Journal of Optimization and Control: 19. Chang CW, Qureshi S, Argyros IK, Saraz KM,
Theories & Applications. 2023;13(2):205-213. Hincal E. A modified fractional Newton’s solver,
https://doi.org/10.11121/ijocta.2023.1260 Axioms. 2024;13(10):689.
9. Evirgen F, Ucar E, Ucar S, Ozdemir N. Mod- https://doi.org/10.3390/axioms13100689
elling influenza a disease dynamics under Caputo- 20. Zhang H, Zhang M, Liu F, Shen M. Review
Fabrizio fractional derivative with distinct con- of the Fractional Black-Scholes Equations and
tact rates, Mathematical Modelling and Numeri- Their Solution Techniques, Fractal and Frac-
cal Simulation with Applications. 2023;3(1):58-73. tional. 2024;8(2):101.
https://doi.org/10.53391/mmnsa.1274004 https://doi.org/10.3390/fractalfract8020101
10. Evirgen F. Transmission of Nipah virus dynam- 21. Li W. The numerical solution of fractional order
ics under Caputo fractional derivative, Jour- equation in financial models and its application
nal of Computational and Applied Mathematics. (Master’s thesis), Hangzhou University of Elec-
2023;418:114654. tronic Science and Technology. 2009;
https://doi.org/10.1016/j.cam.2022.114654 22. Elbeleze AA, Kilicman A, Taib BM. Homotopy
11. Baltaeva U, Babajanova Y, Agarwal P, Ozdemir perturbation method for fractional Black-Scholes
N. Solvability of a mixed problem with the inte- European option pricing equations using Sumudu
gral gluing condition for a loaded equation with transform, Mathematical Problems in Engineer-
the Riemann-Liouville fractional operator, Jour- ing, Article ID 524852. 2013;
nal of Computational and Applied Mathematics. https://doi.org/10.1155/2013/524852
242