Green functions of Fractional Partial Differential Equation With a Modified Elliptic Potential By a Weighted Bessel Function

Abstract

In this paper, the Green function of a fractional partial differential equation [(−Δ)1+α +V (x)]Ψ = δ(x − a), α ∈ (0, 1) is obtained where the Laplacian Δ, 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.