Numerical solution of fredholm fractional integro-differential equation with right-sided caputo’s derivative using bernoulli polynomials operational matrix of fractional derivative - Loh, Jian Rong; Phang, Chang (Springer, 2019)
In this article, fractional integro-differential equation (FIDE) of Fredholm type involving right-sided Caputo’s fractional derivative with multi-fractional orders is considered. Analytical expressions of the expansion coefficient ck by Bernoulli polynomials approximation have been derived for both approximation of single- and double-variable function. The Bernoulli polynomials operational matrix of right-sided Caputo’s fractional derivative Pα −;B is derived. By approximating each term in the Fredholm FIDE with right-sided Caputo’s fractional derivative in terms of Bernoulli polynomials basis, the equation is reduced to a system of linear algebraic equation of the unknown coefficients ck. Solving for the coefficients produces the approximate solution for this special type of FIDE.