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We are concerned with the integrodifferential equation (IDE)α: u(t, x)=O(x)+tα /2 /Γ(1+α/2)ψ(x)+1/Γ(α)∫ o t (t-s)α -1 Δu(s, x)ds for 1≤α≤2. Here Γ(x) is the gamma fonction and Δ=(∂/∂x) 2 . When ψ=0, (IDE) 1 is reduced to the heat equation. For α=2, (IDE) 2 is just the wave equation. The aim of the present paper is to investigate the structure of the solution of (IDE)α by its decomposition for every α, 1≤α≤2

INTEGRODIFFERENTIAL EQUATION WHICH INTERPOLATES THE HEAT EQUATION AND THE WAVE EQUATION I(Martingales and Related Topics)