Abstract
The work reported here concerns the study of a generalized nonlinear fractional boundary value problem involving theta-fractional derivative in the Riemann-Liouville sense. The existence and uniqueness of positive solutions to the problem at hand are proved. Our discussion relies on the properties of Green's function, the upper and lower solutions method, and the classical fixed point theorems in a cone. Moreover, building upper and lower control functions has an effective role in the analysis. Some examples are given to justify the validity of theoretical results.