[1] I. Ahmad, R. Jan, N.N. Razak, A. Khan, T. Abdeljawad, Exploring fractional-order models in computational finance via an efficient hybrid approach, Eur. J. Pure Appl. Math. 18 (2025) 5793.
[2] I. Ahmad, M.N. Khan, R. Jan, N.N. Razak, Efficient numerical method for pricing multi-asset options with the time-fractional Black-Scholes model: focus on American and digital options, Math. Model. Control 5 (2025) 147–163.
[3] P. Amster, C.G. Averbuj, M.C. Mariani, D. Rial, A Black-Scholes option pricing model with transaction costs, J. Math. Anal. Appl. 303 (2005) 688–695.
[4] S. Banihashemi, A. Ghasemifard, A. Babaei, On the numerical option pricing methods: fractional Black-Scholes equations with CEV assets, Comput. Econ. 64 (2024) 1463–1488.
[5] G. Barles, H.M. Soner, Option pricing with transaction costs and a nonlinear Black-Scholes equation, Finance Stoch. 2 (1998) 369–397.
[6] J. Cheridito, Regularizing fractional Brownian motion with a view toward stock pricing modeling, Ph.D. Dissertation, ETH Zurich, 2001.
[7] P. Cheridito, Arbitrage in fractional Brownian motion models, Finance Stoch. 7 (2003) 533–553.
[8] A. Chockalingam, K. Muthuraman, An approximate moving boundary method for American option pricing, Eur. J. Oper. Res. 240 (2015) 431–438.
[9] R. Company, V. Egorova, L. Jodar, C. Vazquez, Finite difference methods for pricing American put option with rationality parameter: Numerical analysis and computing, J. Comput. Appl. Math. 304 (2016) 1–17.
[10] R.H. De Staelen, A.S. Hendy, Numerically pricing double barrier options in a time-fractional Black-Scholes model, Comput. Math. Appl. 74 (2017) 1166–1175.
[11] Z. Ding, C. Granger, R. Engle, A long memory property of stock market returns and a new model, J. Empir. Finance 1 (1993) 83–106.
[12] B. During, M. Fournie, A. Jungel, High order compact finite difference schemes for a nonlinear Black-Scholes equation, Int. J. Theor. Appl. Finance 6 (2003) 767–789.
[13] S. Fallah, F. Mehrdoust, A study of American options under stochastic volatility and double exponential jumps, J. Math. Model. 13 (2025) 467–484.
[14] P. Guasoni, No arbitrage under transaction costs, with fractional Brownian motion and beyond, Math. Finance 16 (2006) 569–582.
[15] Y.A. Kuznetsov, The absence of arbitrage in a model with fractal Brownian motion, Russ. Math. Surv. 54 (1999) 847–848.
[16] D.P. Leisen, Pricing the American put option: A detailed convergence analysis for binomial models, J. Econ. Dyn. Control 22 (1998) 1419–1444.
[17] H.E. Leland, Option pricing and replication with transactions costs, J. Financ. 40 (1985) 1283–1301.
[18] H.K. Liu, J.J. Chang, A closed-form approximation for the fractional Black-Scholes model with transaction costs, Comput. Math. Appl. 65 (2013) 1719–1726.
[19] A.W. Lo, Long-term memory in stock market prices, Econometrica 59 (1991) 1279–1313.
[20] B. Mandelbrot, J.V. Ness, Fractional Brownian motions, fractional noises and applications, SIAM Rev. 10 (1968) 422–437.
[21] H. Mesgarani, S. Ahanj, Y. Esmaeelzade Aghdam, Numerical investigation of the time-fractional Black-Scholes equation with barrier choice of regulating European option, J. Math. Model. 10 (2022) 1–10.
[22] Y. Mishura, Stochastic Calculus for Fractional Brownian Motion and Related Process, Springer, 2008.
[23] Y.S. Mishura, E. Valkeila, The absence of arbitrage in a mixed Brownian-fractional Brownian model, Tr. Mat. Inst. im. V. A. Steklova 237 (2002) 224–233.
[24] A. Neisy, M. Bidarvand, An inverse finance problem for estimating volatility in American option pricing under jump-diffusion dynamics, J. Math. Model. 7 (2019) 287–304.
[25] Z.U. Rehman, S. Boulaaras, R. Jan, I. Ahmad, S. Bahramand, Computational analysis of financial system through non-integer derivative, J. Comput. Sci. 75 (2024) 102204.
[26] M. Rezaei, A.R. Yazdanian, A. Ashrafi, S.M. Mahmoudi, Numerically pricing nonlinear time fractional Black-Scholes equation with time-dependent parameters under transaction costs, Comput. Econ. 60 (2022) 243–280.
[27] M. Rezaei, A.R. Yazdanian, S.M. Mahmoudi, A. Ashrafi, A compact difference scheme for time fractional Black-Scholes equation with time-dependent parameters under the CEV model: American options, Comput. Methods Differ. Equ. 9 (2021) 523–552.
[28] L.C.G. Rogers, Arbitrage with fractional Brownian motion, Math. Finance 7 (1997) 95–105.
[29] S. Rostek, Option Pricing in Fractional Brownian Markets, Springer Sci. Bus. Media, 2009.
[30] J.C. Strikwerda, Finite Difference Schemes and Partial Differential Equations, SIAM, 2004.
[31] D.Y. Tangman, A. Gopaul, M. Bhuruth, A fast high-order finite difference algorithm for pricing American options, J. Comput. Appl. Math. 222 (2008) 17–29.
[32] J. Wang, J.R. Liang, L.J. Lv, W.Y. Qiu, F.Y. Ren, Continuous time Black-Scholes equation with transaction costs in subdiffusive fractional Brownian motion regime, Physica A 391 (2012) 750–759.
[33] X.T. Wang, E.H. Zhu, M.M. Tang, H.G. Yan, Scaling and long-range dependence in option pricing II: Pricing European option with transaction costs under the mixed Brownian-fractional Brownian model, Physica A 389 (2010) 445–451.
[34] R. Yang, X. Qin, B. Xia, Pricing barrier options with time-dependent parameters and curved boundaries, ISECS Int. Colloquium Comput. Commun. Control Manag. 3 (2008) 299–303.
[35] M. Zahle, Long range dependence, no arbitrage and the Black-Scholes formula, Stoch. Dyn. 2 (2002) 265–280.
[36] P. Zhang, Q. Sun, W.L. Xiao, Parameter identification in mixed Brownian-fractional Brownian motions using Powell's optimization algorithm, Econ. Model. 40 (2014) 314–319.
[37] J. Zhao, M. Davison, R.M. Corless, Compact finite difference method for American option pricing, J. Comput. Appl. Math. 206 (2007) 306–321.
)