APPROXIMATE SOLUTIONS OF FRACTIONAL FREDHOLM-TYPE INTEGRO-DIFFERENTIAL EQUATIONS WITH CERTAIN ORTHOGONAL POLYNOMIAL

Abstract

This study focused on obtaining the approximate solution of the fractional integro-differential equation using the orthogonal collocation method (OCM) with a certain orthogonal polynomial, constructed in the interval of [0, 1] (where 0 and 1 are in radian) with respect to the weight function ????(????) = ????????????????. The orthogonal collocation method (OCM) was adopted as a numerical solver with the generated orthogonal polynomial as basis functions. Numerical experiments with MAPLE 18 showed that the method exhibits
rapid convergence. Also, stability analysis of the method showed that the method is stable with minimal error. Hence, the newly constructed orthogonal polynomial was satisfactorily employed to obtain the approximate solution of fractional integro-differential equations with better error estimates when compared with other methods in the literature.