Numerical solution of the conformable differential equations via shifted Legendre polynomials

Abstract

In this paper, we are concerned with the linear and nonlinear multi-term fractional differential equations. Firstly, a new approximate formula of the conformable fractional derivative is derived. The proposed formula is based on the shifted Legendre polynomials. The spectral Legendre collocation method is presented for solving multi-term fractional differential equations. Here, the fractional derivatives are described in the conformable sense. Convergence analysis and estimate an error upper bound of the obtained approximate formula are given. The validity and the applicability of the proposed technique are shown by numerical examples.