Solution of time fractional Black-Scholes PDE using fractional order generalized Chelyshkov wavelets

Document Type : Research Article

Authors

Department of Mathematics and Computing Technology, National Institute of Technology Patna, Patna, 800005, Bihar, India

Abstract

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.

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References

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Journal of Mathematical Modeling
Volume 14, Issue 3
August 2026
Pages 1169-1196

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