Continuation of Radial Positive Definite Functions and Their Characterization

This paper delves into the extension and characterization of radial positive definite functions non-integer dimensions. We provide a thorough investigation by employing Riemann–Liouville fractional integral Caputo derivatives, enabling comprehensive understanding these functions. Additionally, we introduce secondary based on Bernstein completely monotone The practical significance our study is showcased through an examination positivity fundamental solution space-fractional Bessel diffusion equation, highlighting real-world applicability developed concepts. Through this work, contribute to broader their utility in diverse mathematical applied contexts.