Journal
CHAOS SOLITONS & FRACTALS
Volume 105, Issue -, Pages 111-119Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.chaos.2017.10.020
Keywords
Caputo-Fabrizio derivative; Fractional Adams-Bashforth method; Error analysis; Nonlinear chaotic systems; Numerical simulations
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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 a. (0, 1). (C) 2017 Elsevier Ltd. All rights reserved.
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