Existence and Uniqueness of Nonlinear Multi-order Fractional Differential Equations via Green Function

Abstract

This paper is devoted to the study of nonlinear multi-order fractional differential equation of fractional order \( q \in [2,3) \). Firstly, the Green function involving two-parametric Mittag–Leffler function is determined. Then, the existence and uniqueness is obtained using fixed point theorems. The proofs are based upon the reduction of boundary value problem to the equivalent integral equation.