Existence and Estimates of Positive Solutions for Some Singular Fractional Boundary Value Problems - Habib Mâagli; Noureddine Mhadhebi; Noureddine Zeddini (Abstract and Applied Analysis)
We establish the existence and uniqueness of a positive solution u for the following fractional boundary value problem:Dαu(x)=−a(x)uσ(x), x∈(0,1) with the conditions limx→0+⁡x2−αu(x)=0, u(1)=0, where 1<α≤2, σ∈(−1,1), and a is a nonnegative continuous function on (0,1) that may be singular at x=0 or x=1. We also give the global behavior of such a solution.