We propose a COVID-19 mathematical model related to functional shape with square root susceptible-infected interaction. Using the Hurwitz criterion and then a graph theoretical-method for the construction of a Lyapunov function, we discuss both local and global stability. The analytical solution of the system is obtained in a special case. A non-standard finite difference scheme is then developed with the aim to obtain a proper discrete-time version of the model. Simulations show a good agreement between the proposed discretization and the results given by standard numerical methods.

<abstract><p>In this article, we study the existence and uniqueness results for a sequential nonlinear Caputo fractional sum-difference equation with fractional difference boundary conditions by using the Banach contraction principle and Schaefer's fixed point theorem. Furthermore, we also show the existence of a positive solution. Our problem contains different orders and four fractional difference operators. Finally, we present an example to display the importance of these results.</p></abstract>

In this paper, we investigate the controllability of the system with non-local conditions. The existence of a mild solution is established. We obtain the results by using resolvent operators functions, the Hausdorff measure of non-compactness, and Monch’s fixed point theorem. We also present an example, in order to elucidate one of the results discussed.

In this paper, we present some properties of the forward (α, β)-difference operators, and the existence results of two nonlocal boundary value problems for second-order forward (α, β)-difference equations. The existence and uniqueness results are proved by using the Banach fixed point theorem, and the existence of at least one positive solution is established by using the Krasnoselskii' fixed point theorem.