Monotone Theory for Hadamard Fractional Boundary Value Problems

Abstract

In this paper, we study the existence and uniqueness of a weak solution for a fractional differential problem involving the Hadamard fractional derivative, defined on a bounded interval. The initial conditions are assumed to be homogeneous, and the right-hand side is continuous. The analysis is carried out within an appropriate functional framework, and the main results are established by applying the Minty–Browder theorem, which serves as an effective tool for proving the solvability of equations of this type.