A Chebyshev spectral method based on operational matrix for fractional differential equations involving non-singular Mittag-Leffler kernel
Date
2018
Authors
Baleanu, D.
Shiri, B.
Srivastava, H.M.
Al Qurashi, M.
Journal Title
Journal ISSN
Volume Title
Publisher
Advances in Difference Equations
Abstract
In 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.
Description
Keywords
System of fractional differential equations, Chebyshev polynomials, Operational matrices, Mittag-Leffler function, Clenshaw–Curtis formula
Citation
Baleanu, 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/s13662-018-1822-5