The connection of graph and group is a new interesting topic in which the group elements are the graph's vertex set. The non-commuting graph for dihedral groups is one graph representation of the group. This research focuses on the spectral properties of this graph, including spectral radius and energy, in which the matrix representations are distance, Harary, distance Laplacian, and distance signless Laplacian matrices. The relationships between the obtained energies are also presented in this paper.
In this work, in order to better understand the dynamic movement of individuals on the spread of the heroin epidemic in a susceptible population, we formulate a compartmental model of heroin consumption of the SIHR type. After the basic properties, we determine the equilibrium points and we calculate the basic reproduction number R0. We then show local and global stability of the drug-free equilibrium for R-0 < 1. We establish the global stability of the endemic equilibrium for R-0 > 1 by using the appropriate Lyapunov functional method and the LaSalle invariance theorem. We also perform sensitivity analysis of R-0. From numerical simulations, we illustrate our theoretical results analysis. Our main contribution consists to study the impact of adding the remove and decease to the model in and the return to the susceptible state after recovery on the dynamics of heroin transmission in the population.
We investigate an inverse source problem for a timefractional diffusion equation in the whole space R-2 involving the CaputoFabrizio derivative. The problem is ill-posed in the sense of Hadamard. To overcome this difficulty, we employ the mollification method to regularize the final data and reconstruct the unknown source term. Stability estimates and error bounds for the regularized solutions are established, and the optimality of the convergence order is also discussed.
In this article, some theorems related to the common fixed point of four mappings in the setting of rectangular complex-valued metric spaces are proved. The main concern is the extension, generalization and improvement of some fixed point theorems in the present literature on metric fixed point theory for weakly compatible mappings.
This paper investigates the existence of solutions for a class of interval-valued Caputo fractional integro-differential equations with impulses and length constraints. Within the short-memory fractional derivative framework, a hybrid impulse-integral regulatory mechanism is introduced, which integrates continuous integral perturbations with discrete impulses to smooth system dynamics and enhance stability. By applying Schauder's fixed point theorem, the existence of both forward and backward solutions for impulsive interval-valued fractional integro-differential equations is established. These results are further extended to systems with bounded length, yielding existence theorems under length-constrained conditions. We provide numerical examples to demonstrate the theoretical results and the method's applicability to systems with memory effects and uncertainties.
