We prove the solvability of the Cauchy problem for a nonlocal heat equation which is of fractional order both in space and time. The representation formula for classical solutions for time- and space- fractional partial differential operator Dat + a2 (-Δ) γ/2 (0 ≤ α ≤ 1, γ ε (0, 2]) and deviation time variable is given in terms of the Fox H-function, using the step by step method.