In this paper, we present an innovative 3D fractional Hénon-based memristor map and conduct an extensive exploration and analysis of its dynamic behaviors under commensurate and incommensurate orders. The study employs diverse numerical techniques, such as visualizing phase portraits, analyzing Lyapunov exponents, plotting bifurcation diagrams, and applying the sample entropy test to assess the complexity and validate the chaotic characteristics. However, since the proposed fractional map has no fixed points, the outcomes reveal that the map can exhibit a wide range of hidden dynamical behaviors. This phenomenon significantly augments the complexity of the fractal structure inherent to the chaotic attractors. Moreover, we introduce nonlinear controllers designed for stabilizing and synchronizing the proposed fractional Hénon-based memristor map. The research emphasizes the system’s sensitivity to fractional-order parameters, resulting in the emergence of distinct dynamic patterns. The memristor-based chaotic map exhibits rich and intricate behavior, making it a captivating and significant area of investigation.

This paper introduces the concept of multiple attribute decision making (MADM) using q-rung square root interval valued neutrosophic sets (q-rung SRIVNS). The interval valued neutrosophic set (IVNS) and the q-rung square root neutrosophic set (q-rung SRNS) deals with the q-rung SRIVNS. The purpose of this article is to provide an analysis of several aggregating operations. In this article, we discuss a novel idea for the q-rung square root interval valued neutrosophic weighted averaging (q-rung SRIVNWA), q-rung ortho square root interval valued neutrosophic weighted geometric (q-rung SRIVNWG), generalized q-rung SRIVN weighted averaging (q-rung GSRIVNWA) and generalized q-rung SRIVN weighted geometric (q-rung GSRIVNWG). Using Euclidean distances and Hamming distances is illustrated with examples. These sets will be subjected to various algebraic operations in this communication. By doing this, models will be more accurate and will be closed to an integer q. The four most important factors for courier services in India are reliability, turnaround time, payment options, and tracking capabilities. Expert judgments and criteria will determine the most appropriate options. Furthermore, several proposed and current models are compared to demonstrate their reliability and utility. A fascinating and intriguing conclusion can be drawn from the study.

The paper is devoted to the study of graded-simple modules and gradings on simple modules over finite-dimensional simple Lie algebras. In general, a connection between these two objects is given by the so-called loop construction. We review the main features of this construction as well as necessary and sufficient conditions under which finite-dimensional simple modules can be graded. Over the Lie algebra sl2(C), we consider specific gradings on simple modules of arbitrary dimension.

The concept of A-curves is considered as a novel application of real field extensions in solving some algebraic vectorial equations defined by Euclidean norms. In this paper, we present a novel insight through the classification of A-curves by illustrating many new semi-module isomorphisms between the direct product of weak fuzzy complex numbers with itself and the direct product of classical Euclidean vector spaces multiplied by itself. These isomorphisms will give us a full classification of A-curves that are related to weak fuzzy complex ring. Also, we provide many examples to explain the contribution of our work.

American scientific publishing group