New numerical approximation of fractional derivative with non-local and non-singular kernel: Application to chaotic models

• Published in: European physical journal plus Vol. 132; no. 10; p. 444
• Main Authors: Toufik, Mekkaoui, Atangana, Abdon
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2017; Springer Nature B.V
• Subjects: Algorithms; Applied and Technical Physics; Approximation; Atomic; Calculus; Complex Systems; Condensed Matter Physics; Differential equations; Differentiation; Error analysis; Exact solutions; Fractional calculus; Mathematical and Computational Physics; Molecular; Optical and Plasma Physics; Ordinary differential equations; Partial differential equations; Physics; Predictor-corrector methods; Regular Article; Theoretical
• ISSN: 2190-5444; 2190-5444
• DOI: 10.1140/epjp/i2017-11717-0

. Recently a new concept of fractional differentiation with non-local and non-singular kernel was introduced in order to extend the limitations of the conventional Riemann-Liouville and Caputo fractional derivatives. A new numerical scheme has been developed, in this paper, for the newly established fractional differentiation. We present in general the error analysis. The new numerical scheme was applied to solve linear and non-linear fractional differential equations. We do not need a predictor-corrector to have an efficient algorithm, in this method. The comparison of approximate and exact solutions leaves no doubt believing that, the new numerical scheme is very efficient and converges toward exact solution very rapidly.