A hybrid Chelyshkov wavelet-finite differences method for time-fractional black-Scholes equation

[1] Atkinson K. & Han W. (2009). Theoritical Numerical Analysis, A Functional Analysis Framework. Third Edition. Springer.

[2] Batogna R. G. (2018). Analysis of Option Pricing within the Scope of Fractional Calculus. Doctoral Dissertation.  Department of Mathematics and Applied Mathematics, University of the Free State.

[3] Cen Zh., Huang J., Xu A. & Le A. (2018). Numerical approximation of a time-fractional Black{Scholes equation. Computers & Mathematics with Applications. 75(8). 2874-2887. https://doi.org/10.1016/j.camwa.2018.01.016

[4] Cerda J. (2010). Linear Functional Analysis. American Mathematical Society.

[5] Chen W., Xu X. & Zhu S. P. (2015). Analytically pricing double barrier options based on a time-fractional Black{Scholes equation. Computers and Mathematics with Applications. 69. 1407{1419. http://dx.doi.org/10.1016/j.camwa.2015.03.025

[6] Daftardar-Gejji V. (2019). Fractional Calculus and Fractional Di erential Equations. Springer Nature Singapore Pte Ltd.

[7] Gomez-Aguilar J.F., Razo-Hernandez R. & Granados-Lieberman D. (2014). A physical interpretation of fractional calculus in observables terms: analysis of the fractional time constant and the transitory response. Revista Mexicana de Fisica. 60. 32-38.

[8] Gupta V. & Agarwal R. P. (2014). Convergence Estimates in Approximation Theory. Springer.

[9] Khalouta A. (2022). On the solutions of nonlinear Caputo{Fabrizio fractional partial differential equations arising inapplied mathematics. Journal of Prime Research in Mathematics, 18(2), 42-54.

[10] Khalouta A. (2023). New Technique to Accelerate the Convergence of the Solutions of Fractional Order Bratu-Type Di erential Equations. Journal of Science and Arts, 23(3), 609-624.

[11] Khalouta, A. (2023). New approaches for solving Caputo time-fractional non-linear system of equations describing the unsteady ow of a polytropic gas. International Journal of Nonlinear Analysis and Applications. 14(3). 33-46. https://doi.org/10.22075/ijnaa.2022.26839.3422

[12] Khalouta A. (2023). A novel computational method for solving the fractional SIS epidemic model of two di erent fractional operators. Annals of the University of Craiova, Mathematics and Computer Science Series, 50(1). 136{151. https://doi.org/10.52846/ami.v50i1.1639

[13] Laub A. J. (2005). Matrix Analysis for Scientists & Engineers. SIAM.

[14] Li C. & Cai M. (2019). Theory and Numerical Approximations of Fractional Integrals and Derivatives. SIAM.

[15] Li, C. & Chen, A. (2018). Numerical methods for fractional partial di erential equations. International Journal of Computer Mathematics, 95(6{7), 1048{1099. https://doi.org/10.1080/00207160.2017.1343941

[16] Limaye B. V. (2016). Linear Functional Analysis for Scientists and Engineers. Springer.

[17] Mesgarani H., Bakhshandeh M. & Esmaeelzade Aghdam Y. (2022). The Convergence Analysis of the Numerical Calculation to Price the Time-Fractional Black{Scholes Model. Computational Economics. https://doi.org/10.1007/s10614-022-10322-x

[18] Mesgarani H., Beiranvand A. & Esmaeelzade Aghdam Y. (2021). The impact of the Chebyshev collocation method on solutions of the time-fractional Black{Scholes. Mathematical Sciences. (15). 137-143. https://doi.org/10.1007/s40096-020-00357-2

[19] Mohammadi F. (2018). Numerical solution of systems of fractional delay di erential equations using a new kind of wavelet basis. Comp. Appl. Math. 37: 4122-4144. https://doi.org/10.1007/s40314-017-0550-x

[20] Mohapatra J., Santra S. & Ramos H. (2023). Analytical and Numerical Solution for the Time Fractional Black-Scholes Model Under Jump-Di usion. Computational Economics. Springer. https://doi.org/10.1007/s10614-023-10386-3

[21] Mollahasani N. (2023). A Hybrid Spectral-Finite Di erence Method for Numerical Pricing of Time-Fractional Black{Scholes Equation. Computational Economics. https://doi.org/10.1007/s10614-023-10441-z

[22] Morgado M. L., Rebelo M., Ferras L. L. & Ford N. (2016). Numerical solution for di usion equations with distributed order in time using a Chebyshev collocation method. Applied Numerical Mathematics. http://dx.doi.org/10.1016/j.apnum.2016.11.001

[23] Muscat J. (2014). Functional Analysis; An Introduction to Metric Spaces, Hilbert Spaces, and Banach Algebras. Springer Cham. https://doi.org/10.1007/978-3-319-06728-5

[24] Nuugulu S.M., Gideon F. & Patidar K.C. (2021). A robust numerical solution to a time-fractional Black{Scholes equation. Advances in Di erence Equations. 123. https://doi.org/10.1186/s13662-021-03259-2

[25] Owolabi K. M. & Atangana A. (2019). Numerical Methods for Di erentiation. Springer.

[26] Roul P. (2020). A high accuracy numerical method and its convergence for time-fractional Black-Scholes equation governing European options. Applied Numerical Mathematics. 151. 472-493.

[27] SikoraB. (2023). Remarks on the Caputo fractional derivative. MINUT. 5. 76-84.

[28] Song L. & Wang W. (2013). Solution of the Fractional Black-Scholes Option Pricing Model by Finite Di erence Method. Abstract Applied Analysis. 1-10. https://doi.org/10.1155/2013/194286

[29] SontakkeB. R. & Shaikh A. S. (2015). Properties of Caputo Operator and Its Applications to Linear Fractional Di erential Equations. Journal of Engineering Research and Applications, 5(5), 22-27.

[30] Sugandha A., Rusyaman E., Sukono & Carnia E. (2023). A New Solution to the Fractional Black{Scholes Equation Using the Daftardar-Gejji Method. Mathematics. 11(24):4887. https://doi.org/10.3390/math11244887

[31] Torchinsky A. (2015). Problems in Real and Functional Analysis. American Mathematical Society.

[32] Zhang H., Liu F., Turner I. & Yang Q. (2016). Numerical solution of the time fractional Black{Scholes model governing European options. Computers & Mathematics with Applications. 71(9). 1772-1783. https://doi.org/10.1016/j.camwa.2016.02.007

[33] Zhang K. (2021). Existence and uniqueness of analytical solution of time-fractional Black-Scholes type equation involving hyper-Bessel operator. Mathematical Methods in the Applied Sciences. 44(7). 6164{6177. https://doi.org/10.1002/mma.7177

[34] Zhao H. & Tian H. (2017). Finite di erence methods of the spatial fractional Black{Schloes equation for a European call option. IMA Journal of Applied Mathematics. 82(4). 836-848, https://doi.org/10.1093/imamat/hxx016