Regularization of Weak and Basic Singularities in Fractional Integro-Differential Equations

In this paper, we consider some kind of fractional singular integral equations which they have weak and basic singularities in their kernels. In the first section, singularities are removed by changing of variables and change the order of integrals via Fubini’s theorem. In the second section, singularities are kind of basic. And we cannot remove or weaken them by methods of the first section. We will remove these kinds of singularities by Poiencare—Bertrand formula. In the final section, we consider some fractional basic singular Fredholm integral equations and give an example for Volterra case of fractional singular integral equation.