Page 48 - IJOCTA-15-2
P. 48

Analyzing the Black-Scholes equation with fractional coordinate derivatives using . . .

             23. Kumar S, Kumar D, Singh J. Numerical computa-  34. Dehestani H, Ordokhani Y. Improvement of
                tion of fractional Black-Scholes equation arising in  the spectral method for solving multi-term
                financial market, Egyptian Journal of Basic and   time-space  Riesz-Caputo  fractional  differen-
                Applied Sciences. 2014;1(3-4), 177-183.           tial  equations,  Journal  of  Applied  Analy-
                https://doi.org/10.1016/j.ejbas.2014.10.003       sis   and   Computation.2022;12(6):2600-2620.
             24. Hariharan G, Padma S, Pirabaharan P. An          https://doi.org/10.11948/20220146
                efficient wavelet based approximation method
                                                              35. Sayevand K, Ghanbari N, Masti I. A robust com-
                to time-fractional Black-Scholes European op-
                                                                  putational framework for analyzing the Bloch-
                tion pricing problem arising in financial market,
                                                                  Torrey equation of fractional order, Computa-
                Applied Mathematical Sciences. 2013;7(69):3445-
                                                                  tional and Applied Mathematics. 2021;40(4):1-21.
                3456.
                                                                  https://doi.org/10.1007/s40314-021-01513-7
                https://doi.org/10.12988/ams.2013.35261
                                                              36. Zhang H, Liu F, Turner I, Yang Q. Numerical so-
             25. Marom O, Momoniat E. A comparison of numer-
                                                                  lution of the time-fractional Black-Scholes model
                ical solutions of fractional diffusion models in fi-
                                                                  governing European options, Computers and
                nance, Nonlinear Analysis: Real World Applica-
                                                                  Mathematics with Applications. 2016;71(9):1772-
                tions. 2009;10(6):3435-3442.
                                                                  1783.
                https://doi.org/10.1016/j.nonrwa.2008.10.066
                                                                  https://doi.org/10.1016/j.camwa.2016.02.007
             26. Farnoosh R, Sobhani A, Beheshti MH. Effi-
                cient and fast numerical method for pricing dis-  37. Cen Z, Huang J, Xu A, Le A. Numerical approx-
                crete double barrier option by projection method,  imation of a time-fractional Black-Scholes equa-
                Computers and Mathematics with Applications.      tion, Computers and Mathematics with Applica-
                2017;73(7):1539-1545.                             tions. 2018;75(8):2874-2887.
                https://doi.org/10.1016/j.camwa.2017.01.019       https://doi.org/10.1016/j.camwa.2018.01.016
             27. Zhao H, Tian H. Finite difference methods of the
                                                              38. Masti I, Sayevand K, Jafari H. On epidemiological
                spatial fractional Black-Scholes equation for a Eu-
                                                                  transition model of the Ebola virus in fractional
                ropean call option, IMA Journal of Applied Math-
                                                                  sense. Journal of Applied Analysis & Computa-
                ematics. 2017;82(4):836-848.
                                                                  tion. 2024;14:1625-1647.
                https://doi.org/10.1093/imamat/hxx016
                                                                  https://doi.org/10.11948/20230319
             28. Roul P. A high accuracy numerical method and
                its convergence for time-fractional Black-Scholes  39. Mohammadizadeh F, Georgiev SG, Rozza G, To-
                equation governing European options, Applied      hidi E, Shateyi S. Numerical solution of ψ-Hilfer
                Numerical Mathematics. 2020;151:472-493.          fractional Black-Scholes equations via space-time
                https://doi.org/10.1016/j.apnum.2019.11.004       spectral collocation method, Alexandria Engi-
                                                                  neering Journal. 2023;71:131-145.
             29. Krzyzanowski G, Magdziarz M, Plciniczak L. A
                                                                  https://doi.org/10.1016/j.aej.2023.03.007
                weighted finite difference method for subdiffusive
                Black-Scholes model, Computers and Mathemat-
                                                              Maryam Mahdavi Parsa is a Ph.D. student at de-
                ics with Applications. 2020;80(5);653-670.
                                                              partment of mathematical sciences, Malayer univer-
                https://doi.org/10.1016/j.camwa.2020.04.029
                                                              sity. His research interests include: bio-mathematics,
             30. Golbabai A, Nikan O, Nikazad T. Numerical
                                                              fractional differential equations and approximation
                analysis of time-fractional Black-Scholes Euro-
                                                              methods.
                pean option pricing model arising in financial
                                                                 https://orcid.org/0009-0008-4706-0031
                market, Computational and Applied Mathemat-
                ics. 2019;38(4):1-24.                         Khosro Sayevand is a full professor in applied
                https://doi.org/10.1007/s40314-019-0957-7     mathematics at department of mathematical sciences,
             31. Kemppainen J. Existence and uniqueness of the  Malayer university.  His research interests include:
                solution for a time-fractional diffusion equa-  fractional calculus, modelling, perturbation theory and
                tion,Fractional Calculus and Applied Analysis.  linear programming.
                2011;14(3):411-417.                              https://orcid.org/0000-0002-5397-1623
                https://doi.org/10.2478/s13540-011-0025-5
                                                              Hossein Jafari is a full professor in applied
             32. Chen W, Xu X, Zhu, SP. Analytically pricing
                                                              mathematics.  His research interests include: Bio-
                double barrier options based on a time-fractional
                                                              mathematics, fractional differential equations, Lie
                Black-Scholes equation, Computers and Mathe-
                                                              Symmetry and approximation methods.
                matics with Applications. 2015;69(12):1407-1419.
                https://doi.org/10.1016/j.camwa.2015.03.025      https://orcid.org/0000-0001-6807-6675
             33. Masti I, Sayevand K. On collocation-Galerkin  Iman Masti is a graduated Ph.D. student at depart-
                method and fractional B-spline functions for a  ment of mathematical sciences, Malayer university.
                class of stochastic fractional integro-differential  His research interests include: bio-mathematics, frac-
                equations, Mathematics and Computers in Sim-  tional differential equations and approximation meth-
                ulation. 2024;216:263-287.                    ods.
                https://doi.org/10.1016/j.matcom.2023.09.013     https://orcid.org/0009-0007-4454-5095
                                                           243
   43   44   45   46   47   48   49   50   51   52   53