Abstract
In this paper, we study the following fractional Navier boundary value problem
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where alpha, ss. is an element of (0, 1] such that alpha + ss > 1, D-beta and D-alpha stand for the standard Riemann-Liouville fractional derivatives and a, b are nonnegative constants such that a + b > infinity. The function g is a nonnegative continuous function in [0, infinity) that is required to satisfy some suitable integrability condition. Using estimates on the Green's function and a perturbation argument, we prove the existence of a unique positive continuous solution, which behaves like the unique solution of the homogeneous problem.