EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTIONS FOR NONLINEAR LANGEVIN EQUATION INVOLVING TWOFRACTIONAL ORDERS

In this paper we study the existence and uniqueness of positive solutions for initialvalue problems of nonlinear fractional di erential Langevin equation(0.1) (0.1) ocD {} n:Based on obtained results in previous papers, for the existence and uniqueness, thenonlinear termf needs to satisfy some strongly di cult conditions. By using recentfixed point theorems on mixed monotone operators we get some new light results forexistence and uniqueness of solutions.

Keywords:

Fractional di erential equation , Mixed monotone operator , Langevin equation