Development of Conformable Fractional Numerical Methods of Constant Order using Fractional Power Series Theorem

Abstract

This study aims to employ novel numerical approaches for the constant-order conformable fractional derivative. By utilizing the fractional power series theorem, two innovative numerical techniques have been devised: the constant-order conformable Euler method and the constant-order conformable Runge Kutta 2-stage method. Furthermore, these techniques account for various fractional constant-order derivatives. Different models have been analyzed to demonstrate their behavior under varying constant orders, and their agreement and validation with standard Runge-Kutta and Euler methods have been confirmed. Notably, both methods hold promise for application in fractional financial models. The study includes a comparative analysis of these methods against classical derivatives, supported by tabular data showcasing the numerical outcomes.

Keywords: Conformable constant order derivative; Fractional financial model; Numerical technique; Classical derivative.

2010 Mathematics Subject Classification. 26A25; 26A35