Fractional Bell collocation method for solving linear fractional integro-differential equations

In this study, a collocation method based on the Bell poynomials is introduced for solving linear fractional integro-differential equations. Our aim in this study is to obtain the approximate solution of linear fractional integro-differential equations in the truncated fractional Bell series. Firstly, the fractional Bell functions which are a generalization of the Bell polynomials are expressed in matrix forms. Second, by Caputo derivative, the derivatives of the solution form are created for derivatives in the problem. By using the equal spacing points, we reduce the linear fractional problem to a system of linear algebraic equations. The gained this system is solved and its solutions give the coefficients of fractional Bell series which is the assumed solution. Lastly, error estimation is made and the method is applied to numerical examples.