New Solutions for System of Fractional Integro‐Differential Equations and Abel’s Integral Equations by Chebyshev Spectral Method

Abstract

Chebyshev spectral method based on operational matrix is applied to both systems of fractional integro‐differential equations and Abel’s integral equations. Some test problems, for which the exact solution is known, are considered. Numerical results with comparisons are made to confirm the reliability of the method. Chebyshev spectral method may be considered as alternative and efficient technique for finding the approximation of system of fractional integro‐differential equations and Abel’s integral equations.