Solving Fractional Black-Scholes and Navier-Stokes Equations via a New \frac{t^{\varrho}}{\varrho}-Integral Transform and Residual Power Series

This paper introduces a novel approach for solving two-dimensional time-fractional Navier-Stokes and Black-Scholes equations. The method integrates a new integral transform--based on a generalized power function of the form \frac{t^{\varrho}}{\varrho}-- with the residual power series method. This combined approach, termed the ``generalized integral transform residual power series method,'' utilizes the Katugampola fractional derivative in the Caputo sense. The convergence of the method is rigorously established, and its efficacy, accuracy, and precision are demonstrated through illustrative examples. The results highlight the method's potential for efficiently solving complex fractional partial differential equations across various scientific and engineering disciplines.

کلیدواژه ها:

New \tfrac{t^{\varrho}}{\varrho}-general transform ، Black-Scholes equation ، Navier-Stockes ، Residual Power Series‎