Uniqueness of Solutions for the Initial Value Problem of a Simple Type Riccati Equation with Variable Fractional Order

Abstract

In recent years, researches on the fractional Riccati equation have attracted extensive attention, and many achievements have emerged. However, most of the current works are carried out on the basis of constant fractional order. Here we study the Cauchy problem of one simple type Riccati equation with variable fractional order. By using Gronwall-Bellman inequality and other mathematical tools, we will prove the uniqueness of solutions of this problem.