Positive solutions for a Hadamard-type fractional \(p\)-Laplacian integral boundary value problem (Q6599955)

In this work, the authors consider the existence of positive solutions to a Hadamard-type fractional integral boundary value problem using the fixed point index method and multiplicity of solutions using Leggit-Williams fixed point theorem. \N\NThe authors express the solution of the boundary value problem as a Hammerstein integral equation (Lemma 1, Lemma 2).\N\NThe authors state six initial hypothesis for this work (H1)--(H6). The fixed point index theory is used in Theorem 1 and 3 to prove the existence of at least one positive solution. \N\NThe Leggett-Williams fixed point theorem is used to prove multiplicity of solutions in Theorem 3. The authors state additional three hypothesis (H7)--(H9) which are used in Theorem 3 to prove the existence of at least three positive solution. The work concludes with an example to illustrate the results obtained.