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 D ′ ( 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 ∫ θ π / 2 y ( φ ) cos β φ ( cos θ − cos φ ) α d φ = f ( θ ) , and ∫ 0 ∞ x 1 / 2 g ( x ) y ( x + t ) d x = f ( t ) .