A Predictor-Corrector Algorithm in the Framework of Conformable Fractional Differential Equations

TL;DR

This paper introduces a novel predictor-corrector numerical algorithm based on Adams-Bashforth and Adams-Moulton methods for solving conformable fractional differential equations, addressing limitations of existing methods in fractional calculus.

Contribution

The paper presents the first predictor-corrector algorithm tailored for conformable fractional derivatives, enhancing numerical solutions in fractional calculus.

Findings

Demonstrates improved accuracy over existing methods

Provides a stable and efficient numerical scheme

Applicable to various scientific problems involving fractional derivatives

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, but existing numerical methods might have limitations. This work addresses that gap by introducing a new algorithm specifically designed for the conformable fractional derivative using Adams-Bashforth and Adams-Moulton methods.