Generalized Bessel potential and its application to non-homogeneous singular screened Poisson equation

In this paper, generalized Bessel potential is studied. A generalization is achieved by considering the singular Laplace–Bessel operator instead of the Laplace operator in the construction of the Bessel potential. First, we give some auxiliary statements as weighted plane wave relation and generalized Bochner formula. Next, we consider the Bessel kernel and prove some of its properties. After that, we present the definition and properties of generalized Bessel potential. Finally, we consider the generalized Bessel potential as a solution to the singular screened Poisson equation.