Numerical schemes for a class of singular fractional integro-differential equations

Abstract

We consider a class of fractional integro-differential equations with certain type of singularities at the origin. Using a change of variables we reformulate the original problem as a cordial Volterra integral equation and study the existence, uniqueness and regularity of the exact solution. With the help of the obtained information we construct a collocation based numerical method for finding the approximate solution of the original problem and analyse the convergence and the convergence order of the proposed method. We also give some numerical examples.