This paper appertains the presentation of a Clenshaw–Curtis rule to evaluate highly oscillatory Fredholm integro-differential equations (FIDEs) with Cauchy and weak singularities. To calculate singular integral, unknown function approximated by an interpolation polynomial is rewritten as Taylor series expansion. A system linear FIDEs obtained using equally spaced points collocation solved obtai...

In this work, a class of non-linear weakly singular fractional integro-differential equations is considered, and we first prove existence, uniqueness, smoothness properties the solution under certain assumptions on given data. We propose numerical method based spectral Petrov-Galerkin that handling to non-smooth behavior solution. The most outstanding feature our approach evaluate approximate b...