Sampling Theory Associated With Fractal Sturm–Liouville Equations

In this study, we investigate the sampling theory associated with fractal Sturm–Liouville problems. Specifically, we establish two sampling theorems for fractal transforms. The first theorem identifies the sampling kernel as the solution to a corresponding fractal differential equation, while the second represents it in terms of the Green's function associated with the fractal problem. The theoretical results are supported by several illustrative examples that demonstrate the applicability and effectiveness of the proposed approach.