Occupation and survival probability of a subdiffusive particle in a planar wedge with angle π/3

Abstract

Non-Brownian diffusion occurs in complex media, such as biological materials and amorphous surfaces. This can be modelled by solving the fractional diffusion equation in the relevant boundary conditions. In this paper, time-fractional diffusion equation of order 0 < α < 1 was considered for a wedge with opening angle π/3 with absorbing boundaries on both edges. Starting from the Green's function for the two-dimensional plane, the method of images was used to derive expressions for the occupation probability. From this, an analytic, exact, and closed-form expression was obtained for the survival probability. Both the occupation and survival probabilities were plotted. The effects of varying the fractional parameter α and initial location (r₀, θ₀) on these probabilities were also investigated.