  In this paper we develop an integral equation satisfied by Feynman's
operational calculi in formalism of B. Jefferies and G. W. Johnson. In
particular a "reduced" disentangling is derived and an evolution equation of
DeFacio, Johnson, and Lapidus is used to obtain the integral equation. After
the integral equation is presented, we show that solutions to the heat and
Schrodinger's equation can be obtained from the reduced disentangling and its
integral equation. We also make connections between the Jefferies and Johnson
development of the operational calculi and the analytic Feynman integral.
