Fractional powers of the retarded potential

Abstract

The Fréchet space fractional power theory developed in Schiavone¹ is applied to the retarded potential associated with the three (space)–dimensional wave equation. It is shown that the powers obtained coincide with the corresponding Riesz fractional integral. Standard properties of the fractional integral are deduced from the fractional power theory. An indication of how the techniques developed here may be extended to higher dimensional fractional integrals is given.

Keywords:

• Fractional powers
• Riesz fractional integrals
• retarded potential

AMS(MOS)::

• 47A60
• 35L05
• 47L05