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March 25, 2026Open Access

Green's Functions for Fractional Partial Differential Equations With Modified Elliptic Potentials and Bessel Weights

Puntos clave

The central aim is to derive the Green function for fractional partial differential equations incorporating modified elliptic potentials.
Utilized Green's function approach for fractional partial differential equations
Defined Laplacian and potential over a closed ball in Euclidean space
Employed Fourier and Hankel transform techniques for analytical results
Successfully obtained the Green function expression
Showed application in solving fractional partial differential equations
Highlighted the significance of Bessel weights in elliptic potentials

Resumen

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

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