Existence and Uniqueness of Positive and Bounded Solutions of a Discrete Population Model with Fractional Dynamics

Figure 2

Graph of the solution of the fully discrete model (11) over the spatial domain with , , homogeneous Dirichlet boundary data, and initial profile given by (24). Computationally, we used and . Various derivative orders were used, namely, (solid), (dashed), (dashed-dotted), and (dotted). The solutions were calculated at the times (a) , (b) , (c) , (d) , (e) , and (f) . For convenience, the graphs have been plotted on the domain .

(a)

(b)

(c)

(d)

(e)

(f)