On fractional Langevin equation involving two fractional orders in different intervals - Baghani, Hamid; Nieto, J. (Nonlinear Analysis: Modelling and Control, 2019)
In this paper, we study a nonlinear Langevin equation involving two fractional orders  α ∈ (0; 1] and β ∈ (1; 2] with initial conditions. By means of an interesting fixed point theorem, we establish sufficient conditions for the existence and uniqueness of solutions for the fractional equations. Some illustrative numerical examples are also discussed.