On an Application of Phragmén–Lindelöf Method to Singular Fractional-Order Problem

In this paper, we present a novel approach by utilizing the modified Phragmén–Lindelöf method to study the singular fractional-order problem with singular potentials involving exponential critical growth. The application of this method is rarely seen in the study of such problems. We demonstrate that the area of application of the Phragmén–Lindelöf method extends beyond its typical use in complex-valued iterative processes, wave propagation, and diffusion phenomena. Furthermore, our approach proves the existence and multiplicity of solutions for the aforementioned singular singular fractional-order problem. To illustrate the practical significance of our findings, we provide a concrete example that showcases the usefulness of the obtained results.