Novel Method for Approximating Fixed Point of Generalized α-Nonexpansive Mappings with Applications to Dynamics of a HIV Model

In this paper, we use an existing fixed point iterative scheme to approximate a class of generalized α-nonexpansive mapping in Banach spaces. We also prove weak and strong convergence results for the mapping using the AG iterative scheme. An example of a generalized α-nonexpansive mapping is given to show the validity of the claims. We apply the main results to the approximation of solution of a mixed type Voltera–Fredholm functional nonlinear integral equation and to the spread of HIV modeled in terms of a fractional differential equation of the Caputo type.