Some Aspects of Initial Value Problems Theory for Differential Equations with Riemann–Liouville Derivatives

Some subjects of the well-formed initial value problems for ordinary differential equations with Riemann–Liouville derivatives are discussed. As an example the simplest linear homogeneous differential equation with two fractional derivatives is cited. It's shown, that the requirement of the highest derivative summability influence the value of the lowest derivative order or the initial values in Cauchy type conditions. The specific class of functions, allowing the non-summability of the highest derivative, is introduced. The correctness of the modified Cauchy type problem and initial value problems with local and nonlocal conditions is substantiated.