Cauchy problems for fractional differential equations with Riemann–Liouville fractional derivatives

Existence of Mild Solutions to Nonlocal Fractional Cauchy Problems via Compactness

“…The proof of the next result follows as in [26,27]. (1) , ( ) ∈ ( ) and , ( ) = , ( ) for all ∈ ( ) and ≥ 0.…”

“…In fact, if = and = , then the function → , ( ) is a ( , )-regularized family. Moreover, the function , ( ) satisfies the following functional equation (see [27,28]):…”

New Result on the Critical Exponent for Solution of an Ordinary Fractional Differential Problem

“…Fractional Cauchy problems are important in physics to model anomalous diffusion [35], and one has already shown that some transfer processes in a medium and a universal response of electromagnetic, acoustic, and mechanical influence can be described by the fractional Cauchy problem…”

Study on iterative learning control for Riemann-Liouville type fractional-order systems

“…Recently, existence theory of solutions to fractional differential equations involving Riemann-Liouville derivatives has been investigated in [18,19,20,21]. Some researches about Caputo fractional controlled systems have obtained some interesting results [22,23,24,25].…”