A fractional order time‐independent form of the wave equation or diffusion equation in two dimensions is obtained from the standard time‐independent form of the wave equation or diffusion equation in two‐dimensions by replacing the integer order partial derivatives by fractional Riesz‐Feller derivative and Caputo derivative of order α, β, 1 < ℜ(α) ≤ 2 and 1 < ℜ(β) ≤ 2 respectively. In this paper, we derive an analytic solution for the fractional time‐independent form of the wave equation or diffusion equation in two dimensions in terms of the Mittag‐Leffler function. The solutions to the fractional Poisson and the Laplace equations of the same kind are obtained, again represented by means of the Mittag‐Leffler function. In all three cases, the solutions are represented also in terms of Fox′s H‐function.