Conformable Laplacian and fundamental constants: A new perspective on Coulomb and gravitational potentials in D-dimensional space

In this paper, we investigate the solution of the conformable Laplace equation, [Formula: see text] within a D-dimensional space, where the order of the conformable derivative satisfies [Formula: see text]. The conformable scalar potential [Formula: see text] is expressed in terms of the conformable Gegenbauer polynomials. Furthermore, we derive generalized expressions for the Coulomb constant k and the gravitational constant G as functions of the fractional order [Formula: see text]. It is shown that these expressions reduce to their classical values in the limit [Formula: see text], thereby recovering the standard results of classical potential theory.