Hyperbolic Riesz B-Potential and Solution of an Iterated Non-Homogeneous B-Hyperbolic Equation

摘要

Marcel Riesz has created a new method to solve non-homogeneous linear equations, generalizing the fractional Riemann-Liouville integral. We generalize and apply this method to solve linear equations with Bessel operators acting with respect to all variables. This method includes the overcoming of difficulties of the theory of differential equations, caused by the occurrence of divergent integrals. Namely, in some cases (for example, for hyperbolic equations), it is necessary to use the analytical continuation of a potential analytically depending on a parameter.