A solution method for integro-differential equations of conformable fractional derivative

Abstract

Original scientific paper https://doi.org/10.2298/TSCI170624266BThe aim of this work is to determine an approximate solution of a fractional order Volterra-Fredholm integro-differential equation using by the Sinc-collocation method. Conformable derivative is considered for the fractional derivatives. Some numerical examples having exact solutions are approximately solved. The comparisons of the exact and the approximate solutions of the examples are presented both in tables and graphical forms.

Solitary Wave Solutions of Some Conformable Time-Fractional Coupled Systems via an Analytic Approach

“…It is famous that there are precise definitions of fractional Integral and fractional derivatives, which includes, Grünwald-Letnikov, Riesz, Riemann-Liouville (RL), Caputo, Hadamard and Erdélyi-Kober and lots of others [30][31][32]. The fractional CVIM has been carried out in many models with the aid of many authors [33][34][35]. In this work we shall mainly focus on behavior of CVIM.…”

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.…”

Asymptotical stability analysis of conformable fractional systems

“…Fractional differential systems have gained considerable popularity due to its important applications in physics and engineering [1][2][3][4][5][6][7][8] etc. In recent years, several types of fractional definitions are given, such as Riemann-Liouville, Grunwald-Letnikov and Caputo's fractional definition and so on.…”