Positive solutions for fractional differential equations with variable coefficients

In this article, we study the existence of the positive solutions for a class of differential equations of fractional order with variable coefficients. The equation of this type plays an important role in the description and modeling of control systems, such as $PD^{mu}$-controller. The differential operator is taken in the Riemann-Liouville sense. Our analysis relies on the Leggett-Williams fixed point theorem.