An integral boundary fractional model to the world population growth

Abstract

We consider a fractional differential equation of order $\alpha$, $\alpha \in (2,3]$, involving a $\psi$-Caputo fractional derivative subject to initial conditions on function and its first derivative and an integral boundary condition that depends on the unknown function. As an application, we investigate the world population growth. We find an order $\alpha$ and a function $\psi$ for which the solution of our fractional model describes given real data better than available models.