Explicit Solution of Time Fractional Nonlocal Heat Equation

We study a one-dimensional fractional diffusion equation with the Caputo time-derivative of order μ ∈ (0, 1].Applying spectral projectors, we find a series solution of the problem for a special choice of the initial function.Then, using operational calculus approach of Dimovski, we obtain an explicit representation of the solution in the general case.The expression obtained contains a non-classical convolution product of the particular solution and an arbitrary initial function.This result is an extension of the classical Duhamel principle, but for the space variable.