A numerical algorithm for the solution of nonlinear fractional differential equations via beta‐derivatives

Abstract

In this paper, the sinc‐collocation method (SCM) is investigated to obtain the solution of the nonlinear fractional order differential equations based on the relatively new defined fractional derivative, beta‐derivative. For this purpose, a theorem is proved for the approximate solution obtained from the SCM. Moreover, convergence analysis of the SCM is presented. To show the efficiency and the simplicity of the proposed method, some examples are solved, and the results are compared with the exact solutions of the considered equations.

Approximate analytical solutions of a class of non-linear fractional boundary value problems with conformable derivative

“…Some of them are the Caputo derivative, the Riemann-Liouville derivative, Atangana-Baleanu-Caputo derivative, the Caputo-Fabrizio derivative, beta derivative and conformable derivative. Several applications for those derivatives are developed in references [3,4,5,6,7,8,9,10,11,12,13]. In this paper, conformable definition of fractional derivative defined in [14] is considered.…”