Nontrivial solutions for a fractional differential equation with nonlocal Riemann-Stieltjes boundary conditions

The model of fractional differential equation arises from various fields of physics, engineering, and applied mathematics. In this paper, we focus on the existence and uniqueness of nontrivial solutions for a abstract model of fractional differential equation with nonlocal Riemann-Stieltjes boundary conditions. Under certain suitable growth conditions, we establish some sufficient conditions for the existence and uniqueness of nontrivial solutions based on Leray-Schauder nonlinear alternative and Schauder fixed point theorem.