Baleanu, D.Shiri, B.Srivastava, H.M.Al Qurashi, M.2019-03-302019-03-3020182018Baleanu, D., Shiri, B., Srivastava, H.M. & Qurashi, M.A. (2018). A Chebyshev spectral method based on operational matrix for fractional differential equations involving non-singular Mittag-Leffler kernel. Advances in Difference Equations, 2018:353. https://doi.org/10.1186/s13662-018-1822-5https://doi.org/10.1186/s13662-018-1822-5http://hdl.handle.net/1828/10678In this paper, we solve a system of fractional differential equations within a fractional derivative involving the Mittag-Leffler kernel by using the spectral methods. We apply the Chebyshev polynomials as a base and obtain the necessary operational matrix of fractional integral using the Clenshaw–Curtis formula. By applying the operational matrix, we obtain a system of linear algebraic equations. The approximate solution is computed by solving this system. The regularity of the solution investigated and a convergence analysis is provided. Numerical examples are provided to show the effectiveness and efficiency of the method.enSystem of fractional differential equationsChebyshev polynomialsOperational matricesMittag-Leffler functionClenshaw–Curtis formulaArticleDepartment of Mathematics and Statistics