In this article, the properties of solutions of Hadamard fractional differential equations are investigated on an infinite interval. The equations are subject to integral and discrete boundary conditions. A new proper compactness criterion is introduced in a unique space. By applying the monotone iterative technique, we have obtained two positive solutions. And, an error estimate is also shown at the end. This study innovatively uses a monotonic iterative approach to study Hadamard fractional boundary-value problems containing multiple fractional derivative terms on infinite intervals, and it enriches some of the existing conclusions. Meanwhile, it is potentially of practical significance in the research field of computational fluid dynamics related to blood flow problems and in the direction of the development of viscoelastic fluids.

The purpose of this article is to investigate a class of nonlinear p-Laplacian Hadamard fractional differential equations. By employing two fixed–point theorems of the sum operator, we get the uniqueness of a positive solution for such p-Laplacian equations. In addition, an iterative sequence can be constructed to approximate the unique positive solution. The validity of the results is demonstrated through two illustrative numerical examples in the final of this paper.