Monotone iterative sequences for positive solutions of a p-Laplacian Hadamard fractional boundary value problem on an unbounded domain

Abstract

In this paper, we ensure the existence and uniqueness of positive solutions for a Hadamard fractional boundary value problem with the p-Laplacian operator on an unbounded domain. The problem is formulated as a nonlinear differential equation involving a fractional derivative of order ℓ ∈ (n – 1, n], n ∈ N, along with boundary conditions of the Hadamard fractional integral and derivative. Using the monotone iterative technique, we establish the existence of positive solutions by constructing monotone sequences that approach the solution. An error estimation formula is provided. An example is also discussed to illustrate the main result.