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

In this paper, the Green function of a fractional partial differential equation [(−∆)1+α + V (x)]Ψ = δ(x−a),α ∈ (0,1) is obtained where the Laplacian ∆, the potential V (x) and the Dirac delta function δ(x) are defined over a closed ball B(0,r) of radius r > 0 in an Euclidean space Rn and V (x) is a modified vector-valued Weierstrass sigma elliptic potential weighted by a Bessel function. A combination of Fourier and Hankel transform techniques are employed in obtaining the main result.