On a new predictor-corrector scheme for solving nonlinear differential equations with conformable fractional derivative operator

Abstract

This work proposes a conformable fractional predictor-corrector algorithm for solving conformable fractional differential equations. Fractional calculus is finding applications in various scientific fields; therefore, developing numerical methods to solve fractional differential equations that model natural phenomena is of high importance, especially when finding analytical solutions is of high difficulty. Many authors have developed numerical methods for other fractional derivatives, such as the Caputo fractional derivative. In this article, our aim is to design Adams-Bashforth and Adams-Moulton methods specifically tailored for the conformable fractional derivative. Some examples are provided to illustrate the applicability of the numerical method.