Efficiency of new Canonical polynomials in Solving nonlinear Fractional Integro-Differential equations

This paper is aimed to solve nonlinear fractional integro-differential equations, specifically of the Volterra-types, utilizing newly constructed versatile canonical polynomials. The technique involves the use of the Lanczos method. The popular numerical method known as the collocation method is presented to evaluate the evolving equations and subsequently to determine the values of the embedded unknown coefficients. The equations exhibit both derivatives and integrals. The resulting approximate solutions are compared with the given exact solutions. Numerical experiments are conducted to showcase the efficiency and accuracy of the technique, which is achieved by estimating the errors in the approximate solutions in order to significantly establish the convergence of the method. The mathematical tool utilized to obtain the required results is Maple 18 software package.