A New Perspective via Fractional Calculus for the Radial Schr¨odinger Equation

Differintegral theorems are applied to solve some ordinary differential equations and fractional differential equations. By using these theorems, we obtain different results in the fractional differintegral forms. In this paper, we aim to solve the radial Schr¨odinger equation under the 2 κ potential V (r) = H/r − K/r + Lr in κ = 0, −1, −2 cases. We also obtain the solutions in the hypergeometric forms.