In this paper, we study two mathematical models, involving delay differential equations, which describe the processes of erythropoiesis and leukopoiesis in the case of maintenance therapy for acute lymphoblastic leukemia. All types of possible equilibrium points were determined, and their stability was analyzed. For some of the equilibrium points, conditions for parameters that imply stability were obtained. When this was not feasible, due to the complexity of the characteristic equation, we discuss the stability through numerical simulations. An important part of the stability study for each model is the examination of the critical case of a zero root of the characteristic equation. The mathematical results are accompanied by biological interpretations.

In this paper, we use a generalized form for the Jordan totient function in order to extend the Reciprocal power GCDQ matrices and power LCMQ matrices from the standard domain of natural integers to Euclidean domains. Structural theorems and determinantal arguments defined on both arbitrary and factor-closed q-ordered sets are presented over such domains. We illustrate our work in the case of Gaussian integers.

This article delves into the analysis of nonlinear implicit ω-Caputo fractional-order ordinary differential equations (NLIFDEs) with two-point fractional derivatives and integral boundary conditions within the context of Banach algebra. The primary focus is on demonstrating the existence and uniqueness of solutions for these complex fractional differential equations by utilizing Banach's and Krasnoselskii's fixed point theorems. Furthermore, the study explores the stability of these solutions through the Ulam-Hyers and Ulam-Hyers-Rassias stability criteria, thereby assessing the robustness of the proposed model. To illustrate the versatility of the generalized model, several special cases are examined, showcasing its ability to encompass various classical models. The practical applicability of the theoretical findings is underscored through a numerical example, which demonstrates the feasibility and relevance of the proposed methodology. This thorough investigation advances the comprehension of nonlinear fractional differential equations with integral boundary conditions, highlighting the intricate relationship between fractional derivatives, nonlinearities, and integral terms. The results offer significant insights into the behavior and stability of solutions within this demanding mathematical framework.

This article focuses on the complex version of the Bertozzi–Esedoglu–Gillete–Cahn–Hilliard equation for grayscale image inpainting as well as on the multicomponent Cahn–Hilliard systems for image inpainting. That is, the objective is to outline an extension approach for color image inpainting. We study into the well-posedness of the steady state problem associated with the complex Bertozzi–Esedoglu–Gillete–Cahn–Hilliard equation and with the Bertozzi–Esedoglu–Gillete–Cahn Hilliard systems. Then, backward Euler discretization in time is considered in both the models mentioned. We succeed in proving the stability of the backward Euler scheme. Finally, some numerical simulations are performed that confirm the theoretical results and show the efficiency of the scheme. The simulations are done using FreeFem++.