During the last few decades a rapid growth of methods and models based on differential equations of arbitrary order has been observed. This research is, as almost always, motivated in a twofold way - both by the pure mathematical curiosity and by physical phenomena, which adequate description is beyond the classical mathematical modelling. Some of these investigations have given a need for generalizations of the notion of integral and derivative. During this talk I plan to investigate a problem associated with the analysis of differential equations with the fractional derivative. This will be based on my previously published results which develop appropriate mathematical tools and methods. Their main purpose is to transform an integral equation with the fractional derivative into a classical ordinary differential equation. This equation, although more simple, usually cannot be solved analytically. My approach is based on an application of a number of approximation methods such as asymptotic expansions and perturbation theory.