Variable-Order Conformable Fractional Derivatives using 2-stage Runge-Kutta and Euler Methods

Abstract

The present investigation is intended to the implementation of new numerical approaches for the variable-order conformable fractional derivatives that override the fact of earlier constant order fractional derivatives. The generalized conformable variable-order Taylor’s theorem is deployed to extract two new techniques such as conformable variable order 2-stage Runge-Kutta and conformable variable order Euler methods. Further, these numerical techniques are employed by considering various fractional variables as well as constant order derivatives. However, the main attraction of these two methodologies is also applicable to fractional financial model and comparison of these methodologies with classical derivatives, and the numerical results are appended in tabular form as well as graphically.