Application of Two-Dimensional Fibonacci Wavelets in Fractional Partial Differential Equations Arising in the Financial Market

چکیده مقاله

This manuscript provides an efficient and high-accuracy computational technique for solving fractional Black–Scholes equations (FB–SEs) arising in the financial market. In order to find an accurate solution of the mentioned equations, we use the collocation method through the two-dimensional Fibonacci wavelets (2D-FWs). To carry out the scheme, we firstly present 2D-FWs. Then, Riemann–Liouville pseudo-operational matrix for 1 & 2D-FW are achieved. RL pseudo-operational matrix for 2D-FWs and the collocation technique are employed to reduce the mentioned problem into a system of algebraic equations. Moreover, the convergence of the approximate solution to the exact solution is proven by providing an upper bound of error estimate. To reveal the performance and accuracy of the developed method, some numerical experiments are provided. Moreover, we present a brief bibliometric analysis and scientific trends to quantitatively measure research results on considered equations. © 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited.