This paper presents an efficient numerical technique for solving the time-fractional Black-Scholes equation, which models the pricing of European options. The proposed method is based on a fractional order generalized Chelyshkov wavelets (FOGCW), a generalized form of classical wavelets. The computation of the Riemann-Liouville fractional integral operator (RLFIO) is a key point of this method. An exact formulation of RLFIO corresponding to FOGCW is obtained. The RLFIO of the traditional Chelyshkov wavelet has been previously obtained through Laplace transform techniques; however, due to the complex structure of the scaling and modulation parameters of generalized fractional order, this technique does not work. In this work, we have utilized the regularized beta function to derive an exact formula for the RLFIO of FOGCW. Several numerical examples are presented to confirm the accuracy and efficiency of the proposed method. Error analysis is also conducted.
Sabir, S. and Ahmad, A. (2026). Solution of time fractional Black-Scholes PDE using fractional order generalized Chelyshkov wavelets. Journal of Mathematical Modeling, (), -. doi: 10.22124/jmm.2026.32461.2944
MLA
Sabir, S. , and Ahmad, A. . "Solution of time fractional Black-Scholes PDE using fractional order generalized Chelyshkov wavelets", Journal of Mathematical Modeling, , , 2026, -. doi: 10.22124/jmm.2026.32461.2944
HARVARD
Sabir, S., Ahmad, A. (2026). 'Solution of time fractional Black-Scholes PDE using fractional order generalized Chelyshkov wavelets', Journal of Mathematical Modeling, (), pp. -. doi: 10.22124/jmm.2026.32461.2944
CHICAGO
S. Sabir and A. Ahmad, "Solution of time fractional Black-Scholes PDE using fractional order generalized Chelyshkov wavelets," Journal of Mathematical Modeling, (2026): -, doi: 10.22124/jmm.2026.32461.2944
VANCOUVER
Sabir, S., Ahmad, A. Solution of time fractional Black-Scholes PDE using fractional order generalized Chelyshkov wavelets. Journal of Mathematical Modeling, 2026; (): -. doi: 10.22124/jmm.2026.32461.2944
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