Analysis and application of new fractional Adams–Bashforth scheme with Caputo–Fabrizio derivative

Abstract

Recently a new fractional differentiation was introduced to get rid of the singularity in the Riemann-Liouville and Caputo fractional derivative. The new fractional derivative has then generate a new class of ordinary differential equations. These class of fractional ordinary differential equations cannot be solved using conventional Adams–Bashforth numerical scheme, thus, in this paper a new three-step fractional Adams–Bashforth scheme with the Caputo–Fabrizio derivative is formulated for the solution linear and nonlinear fractional differential equations. Stability analysis result shows that the proposed scheme is conditionally stable. Applicability and suitability of the scheme is justified when applied to solve some novel chaotic systems with fractional order α ∈ (0, 1).