[For part I see ibid. 27, No. 2, 309-321 (1990; Zbl 0790.45009).]
We are concerned with the integrodifferential equation
for . When , is reduced to the heat equation. For , is just the wave equation and its solution has the expression called d’Alembert’s formula:
The aim of the present paper is to investigate the structure of the solution of by its decomposition for every , . We show that has the unique solution expressed as
where is the continuous, nondecreasing and nonnegative stochastic process with Mittag-Leffler distribution of order , and stands for the expectation. We remark that the expression (1) has the same form as that of d’Alembert’s formula.