Abstract
Using estimates on the Green function and a perturbation argument, we prove the existence and uniqueness of a positive continuous solution to problem:
where
is the standard Riemann-Liouville fractional derivative,
,
are nonnegative constants such that
> 0 and
) is a nonnegative continuous function that is required to satisfy an appropriate condition related to a class
satisfying suitable integrability condition. We also give a global behavior of such solution.