Comparative Analysis of the Time-Fractional Black-Scholes Option Pricing Equations (BSOPE) by the Laplace Residual Power Series Method (LRPSM)

The residual power series method is effective for obtaining solutions to fractional-order differential equations. However, the procedure needs the n-1 pi derivative of the residual function. We are all aware of the difficulty of computing the fractional derivative of a function. In this article, we considered the simple and efficient method known as the Laplace residual power series method (LRPSM) to find the analytical approximate and exact solutions of the time-fractional Black-Scholes option pricing equations (BSOPE) in the sense of the Caputo derivative. This approach combines the Laplace transform and the residual power series method. The suggested method just needs the idea of an infinite limit, so the computations required to determine the coefficients are minimal. The obtained results are compared in the sense of absolute errors against those of other approaches, such as the homotopy perturbation method, the Aboodh transform decomposition method, and the projected differential transform method. The results obtained using the provided method show strong agreement with different series solution methods, demonstrating that the suggested method is a suitable alternative tool to the methods based on He's or Adomian polynomials.

Automated summary

The article introduces the Laplace residual power series method (LRPSM) as an effective approach for solving fractional-order differential equations. It applies LRPSM to find analytical approximate and exact solutions of the time-fractional Black-Scholes option pricing equations (BSOPE) in the sense of the Caputo derivative. The method combines Laplace transform and residual power series method, requiring minimal computation for coefficient determination, and shows strong agreement with other series solution methods.