Chebyshev Collocation Method for the Fractional Fredholm Integro-Differential Equations

Abstract

In this study, Chebyshev polynomials have been applied to construct an approximation method to attain the solutions of the linear fractional Fredholm integro-differential equations (IDEs). By this approximation method, the fractional IDE has been transformed into a linear algebraic equations system with the aid of the collocation points. In the method, the conformable fractional derivatives of the Chebyshev polynomials have been calculated in terms of the Chebyshev polynomials. Using the results of these calculations, the matrix relation for the conformable fractional derivatives of Chebyshev polynomials was attained for the first time in the literature. After that, the matrix forms have been replaced with the corresponding terms in the given fractional integro-differential equation, and the collocation points have been used to have a linear algebraic system. Furthermore, some numerical examples have been presented to demonstrate the preciseness of the method. It is inferable from these examples that the solutions have been obtained as the exact solutions or approximate solutions with minimum errors.