Abstract

The goal of this paper is to study fractional calculus of distributions, the generalized Abel’s integral equations, as well as fractional differential equations in the distributional space ${\mathcal{D}}^{\prime }(R^{+})$ based on inverse convolutional operators and Babenko’s approach. Furthermore, we provide interesting applications of Abel’s integral equations in viscoelastic systems, as well as solving other integral equations, such as ${\int }_{\theta }^{\pi /2}\frac{y(\phi )}{{\cos }^{\beta }\phi {(\cos \theta -\cos \phi )}^{\alpha }}d\phi =f(\theta )$ , and ${\int }_0^{\infty }{x}^{1/2}g(x)y(x+t)dx=f(t)$ . View Full-Text