In this article, we propose a coupled system of Caputo fractional Hahn difference equations with nonlocal fractional Hahn integral boundary conditions. The existence and uniqueness result of solution for the problem is studied by using the Banach’s fixed point theorem. Furthermore, the existence of at least one solution is presented by using the Schauder fixed point theorem.

In this paper, we prove existence and uniqueness results for a fractional sequential fractional q-Hahn integrodifference equation with nonlocal mixed fractional q and fractional Hahn integral boundary condition, which is a new idea that studies q and Hahn calculus simultaneously.

In the 1950s, a future Nobelist Simon Kuznets discovered the following phenomenon: as a country's economy improves, inequality first grows but then decreases. In this paper, we provide a simple dynamical system-based explanation for this empirical phenomenon. 1 Kuznets Curve: A Brief Reminder and Need for an Explanation What is the Kuznets curve. In the 1950s, Simon Kuznets, an American economist of Russian origin, showed that as the country's Gross Domestic Product (GDP) increases, inequality first increases and then decreases again [1, 2, 4]. The resulting dependence on inequality on GDP looks like an inverted letter U and is thus called an inverted U-shaped dependence or the Kunzets curve. For this work, Professor Kuznets was awarded a Nobel Prize in Economics in 1971. Kuznets curve: a controversy. The Kuznets curve is a purely empirical observation. Economists from different sides of the political spectrum have come up with different (and mutually exclusive) explanations for this empirical fact. On the one hand, free-market champions use the Kuznets curve as an argument that the governments should not interfere with the free market: inequality will decrease by itself, as soon as the economy improves further. As Ronald Reagan used to say, The rising tide lifts all the boats. Based on this argument, these economists

Abstract. Previous work has shown that intracellular delay needs to be taken into account to accurately determine the half-life of free virus from drug perturbation experiments [1]. The delay also effects the estimated value for the infected T-cell loss rate when we assume that the drug is not completely effective [19]. Models of virus infection that include intracellular delay are more accurate representations of the biological data.We analyze a non-linear model of the human immunodeficiency virus (HIV) infection that considers the interaction between a replicating virus, CD4+ T-cell and the cytotoxic-lymphocytes (CTL). We then investigate the intracellular delay effect on the stability of the endemically infected steady state. Criteria are given to ensure that the infected steady state is asymptotically stable for all delays. Model analysis also allows the prediction of a critical delay τ c below which the effector CTL can play a significant role in the immune control mechanism even when the basic reproduction number is high.

In this paper, we aim to study a nonlocal Robin boundary value problem for fractional sequential fractional Hahn-q-equation. The existence and uniqueness results for this problem are revealed by using the Banach fixed point theorem. In addition, the existence of at least one solution is studied by using Schauder’s fixed point theorem. The theorems for existence results are obtained.