Positive solutions for fractional boundary value problems under a
generalized fractional operator
The work reported here concerns with study a generalized nonlinear
fractional boundary value problems involving $ \vartheta
$- 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 the 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 have an
effective role in the analysis. Some examples are offered to justify the
validity of theoretical findings.