Generalized Fox Integral Equations Solved by Functional Equations

Abstract

A Fox integral equation is of the form:

$$ {\rm{p}}\left( {\rm{t}} \right){\rm{ + }}\int\limits_{{\rm{ - }}\infty }^\infty {{\rm{ G}}\left( {{\rm{t + s}}} \right){\rm{p}}\left( {\rm{s}} \right){\rm{ds = }}{{\rm{p}}_{\rm{o}}}\left( {\rm{t}} \right){\rm{, t}} \in {\rm{R}}} $$

((*))

(cf. Fox [1], Titchmarsh [7], p. 332).