A Chebyshev spectral method based on operational matrix for fractional differential equations involving non-singular Mittag-Leffler kernel

By Dumitru Băleanu, Babak Shiri, Hari M. Srivastava, M. A. Qurashi. Advances in Differential Equations, 2018

101 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/d145a0fa5624a5b6c2a93c035133188495f0377c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

Integral inequalities for a fractional operator of a function with respect to another function with nonsingular kernel (2020, background): “After Leibniz, many famous mathematicians and physicians have studied theory and application of this model for fractional derivatives and integrals and fractional differential equations; see for detail [12, 13, 35, 55].”