A novel approach to Caputo–Hadamard pantograph problems in $\mathfrak{L}^{\mathsf{p}}$-spaces

In this paper, we investigate the existence and uniqueness of solutions for Caputo–Hadamard pantograph fractional differential equations with boundary conditions in $\mathfrak{L}^{\mathsf{p}}$ -spaces, by applying fixed-point theorems in $\mathfrak{L}^{\mathsf{p}}$ -spaces to prove existence and uniqueness. Stability is analyzed through the Ulam–Hyers stability and Ulam–Hyers–Rassias stability, offering key insights into the reliability of the system. Practical examples are also provided for illustration.