Nonlocal Hadamard fractional boundary value problem with Hadamard integral and discrete boundary conditions on a half-line

This article investigates a new class of boundary value problems of one-dimensional lower-order nonlinear Hadamard fractional differential equations and nonlocal multi-point discrete and Hadamard integral boundary conditions. By using monotone iterative method, we not only seek the twin positive solutions of the problem but also show that the monotone iterative schemes converge to a unique positive solution of the problem. An error estimate formula is also given. For the illustration of the main results, we construct an example. (C) 2018 Elsevier B.V. All rights