New numerical approximation of fractional derivative with non-local and non-singular kernel: Application to chaotic models
Department of Applied Mathematics, Faculty of Science, Université Moulay Ismail, B.P. 11201, Zitoune Meknès, Morocco
2 Institute for groundwater studied, Faculty of Natural and Agricultural Science, University of Free State, 9300, Bloemfontein, South Africa
Accepted: 12 September 2017
Published online: 30 October 2017
Abstract.: 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.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2017. corrected publication 2022