A Study of Green's Functions in Fractional Pdes With Modified Elliptic Potentials and Bessel Weights

Key Points

• The aim is to derive the Green function for a fractional partial differential equation involving modified elliptic potentials.
• Derived the Green function using techniques combining Fourier and Hankel transforms.
• Focused on a fractional PDE with Laplacian and Dirac delta function definitions.
• Considered a modified vector-valued Weierstrass sigma elliptic potential weighted by a Bessel function.
• The Green function was successfully obtained for the specified fractional PDE.
• Results hold for the domain defined as a closed ball in Euclidean space Rn.
• Potential implications for physical applications involving fractional dynamics were discussed.