Weimin Hu

This paper investigates a class of nonlinear fractional differential equations with boundary value problems involving Caputo–Hadamard-type derivatives. By relaxing the monotonicity constraints on the nonlinear terms and considering more general nonlinear structures, the paper extends the theoretical framework and application scope of the relevant fractional models. Using the upper-lower solution method in conjunction with Schauder’s fixed-point theorem, we establish the existence of exact solutions; furthermore, by applying the Banach contraction mapping principle, we prove the uniqueness of the solutions. Concurrently, we construct a convergent iterative approximation scheme and provide a priori and a posteriori error estimates for numerical solution. Furthermore, the robustness of the solutions to perturbations is characterised via Ulam–Hyers stability analysis, ensuring the reliability of the approximate solutions. Finally, numerical examples are employed to validate all theoretical results. The qualitative theory and numerical analysis methods for Caputo–Hadamard-type fractional boundary value problems have been improved.

This paper investigates a novel class of fractional Langevin equations, which introduces a time-varying p(t)-Laplacian operator and parameterized anti-periodic boundary conditions. This approach overcomes the limitations of traditional models characterized by constant diffusion exponents and fixed boundary locations. Under non-compactness conditions, the existence of solutions is established by applying Schaefer’s fixed-point theorem, which significantly relaxes the conventional constraints on the nonlinear term. Moreover, by imposing a Lipschitz condition on the nonlinear term, a Ulam–Hyers-type stability criterion for the coupled system is derived. This work not only extends the relevant stability theory but also provides a rigorous theoretical foundation for error control in practical applications. The effectiveness of the theoretical results is validated through numerical examples.

Chemical graph theory is an interdisciplinary mathematics and chemistry discipline that obtains mathematical information about the structure of target compounds and is an important research branch in theoretical pharmacology and nanomedicine. This paper study a coupled Hadamard type sequential fractional differential system on glucose graphs and establishes the Ulam's stability and existence of the system solutions. Furthermore, we examine examples against different background graphs and provide approximate graphs of the solutions. The novelty of this paper is that the origin of each edge is not fixed in modeling the glucose graphs, and one of the two vertices of the corresponding edge can be arbitrarily chosen as the origin to build the system and give the approximate graphs of the solutions using iterative methods and numerical simulation.

In this paper, by using fixed-point theorems, the existence and uniqueness of positive solutions to a class of four-point impulsive fractional differential equations with p-Laplacian operators are studied. In addition, three examples are given to justify the conclusion. The interest of this paper is to study impulsive fractional differential equations with p-Laplacian operators.