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Variable-order derivatives are the natural extension of ordinary as well as of fractional-order differentiations and integration, respectively. Numerous suggestions for fractional variable-order operators have been made in the literature over time. Therefore, this is the moment to shine a light on the variable-order fractional calculus, due to the fact that it accurately describes the mathematical underpinnings and emphasizing the modeling utility via using contemporary numerical techniques. This study focuses on investigating a fractional variable-order model of lymphatic filariasis infection using with Atangana–Beleanue–Caputo derivative. Our investigations have led to the development of newly refined results, focusing on both qualitative and numerical aspects of analysis. To achieve our research objectives, we employ the fixed point theorems of Banach and Krasnoselskii. These theorems serve as powerful tools, allowing us to establish results regarding the existence of solutions to the model. Additionally, for precise numerical simulations, we employ the fractional Euler’s method, a sophisticated computational technique that allows us to effectively simulate and interpret the results both numerically and graphically. These graphs illustrate distinct variable-orders, providing a comprehensive understanding of the model’s behavior under different conditions. Here, it should be kept in mind that we have select various continuous functions for variable to present our graphical illustration.

The exploration of peristaltic pumping and heat transfer in magnetohydrodynamic biofluids holds considerable significance with diverse physiological applications, including their use in surgical equipment for the heart, drug injection, cancer therapies, and dialysis. These studies find relevance in various industrial processes, such as the production of pharmaceutical fluids, liquid filtration, and the contamination-free dispensing of cosmetic/glue emulsions. Consequently, the current analysis delves into the intricacies of thermal emission and viscous dissolution in the peristaltic movement of a six-constant Jeffreys magneto-nanofluid within an asymmetric channel. This investigation considers double diffusion convection and incorporates slip conditions. The energy equation is formulated, incorporating features of thermal dispersion and viscous dissolution. The initial model includes a collection of non-linear partial differential equations (PDEs). To simplify the problems, the analysis is made simpler under the supposition of a small Reynolds number and large wavelength, leading to the governing system of PDEs that is further computed using the numerical technique NDSolve. A detailed analysis is conducted for various parameters, including nanoparticle fraction, pressure increase, velocity, temperature, pressure gradient, concentration, and stream functions. Graphical presentations of the obtained results showcase the influence of different flow quantities, noting that the temperature profile boosts due to the growing impact of the increasing concentration of thermal slip, while concentration decreases owing to the increasing concentration of the slip parameter. Moreover, it is also noted that as the thermophoresis parameter, thermal slip parameter, and Brinkman number increase, the temperature profile increases; conversely, it decreases with the thermal radiation parameter. [ABSTRACT FROM AUTHOR]

The complex anti-fuzzy set (CAFS) is an extension of the traditional anti-fuzzy set with a wider range for membership function beyond real numbers to complex numbers with unit disc aims to address the uncertainty of data. The complex anti-fuzzy set is more significant because it provides two dimensional information and versatile representation of vagueness and ambiguity of data. In terms of the characteristics of complex anti-fuzzy sets, we proposed the concept of (ε, δ)-CAFSs that offer a more comprehensive representation of the uncertainty of data than CAFSs by considering both the magnitude and phase of the membership functions and explain the (ε, δ)-complex anti fuzzy subgroups (CAFSG) in the context of CAFSs. Moreover, we showed that every CAFSG is a (ε, δ)-CAFSG. Also, we used this approach to define (ε, δ)-complex anti-fuzzy(CAF) cosets and (ε, δ)-CAF normal subgroups of a certain group as well as to investigate some of their algebraic properties. We elaborated the (ε, δ)-CAFSG of the classical quotient group and demonstrated that the set of all (ε, δ)-CAF cosets of such a particular CAFs normal subgroup formed a group. Furthermore, the index of (ε, δ)-CAFSG was demonstrated and (ε, δ)-complex anti fuzzification of Lagrange theorem corresponding to the Lagrange theorem of classical group theory was briefly examined. [ABSTRACT FROM AUTHOR]

This study aims to address the difficulties in solving coupled generalized non-linear Burger equations using local fractional calculus as a framework. The methodology used in this work, particularly in the area of local fractional calculus, combines the Elzaki transform with the Adomian decomposition method. This combination has proven to be a highly effective strategy for addressing non-linear partial differential equations within the local fractional context, which finds numerous practical applications. The proposed method offers a systematic and easily understandable procedure for tackling both linear and non-linear partial differential equations (PDEs). It provides an easy-to-follow path to solve these problems. We offer a real-world example that exhibits the method's successful use in resolving issues to corroborate its efficacy. The obtained solution is visually represented to illustrate the practical utility of this approach. [ABSTRACT FROM AUTHOR]

In the context of fractal space, this study presents a higher-order nonlinear local fractional Bratu-type equation and thoroughly examines this generalized nonlinear equation. Additional analysis and identification of particular special situations of the generalized local fractional Bratu equation is performed. Finally, the Adomian decomposition method is utilized to derive that solution for the generalized Bratu equation of local fractional type. This study contributes to a deeper understanding of these equations and provides a practical computational approach to their solutions. [ABSTRACT FROM AUTHOR]

Symmetry is a key part of the study of basic forces and particles, as well as the creation of mathematical models that help scientists in various scientific disciplines understand complex events. Scientists can figure out what a system is made of and how it works by looking at its symmetry. They can then use this information to make predictions and create new materials and technologies. Humanity has conquered many once-fatal diseases due to medical research and technological advancements. Although this progress is encouraging, there are still a great many areas that require continual human efforts. An effort is made in this article to choose the best treatment strategy to completely manage the pandemic of COVID-19 under conjunctive complex fuzzy knowledge. In this paper, the concept of conjunctive complex fuzzy relations is presented and numerous set theoretical aspects of this phenomenon are established. The investigation of this ideology is further expanded to describe different sorts of essential structural conjunctive complex fuzzy relations. Matrix and graphical representations of the formation of these newly specified relations are also provided. Moreover, this concept has been successfully employed to provide a therapy strategy for a rapid recovery from COVID-19. Furthermore, a comparative analysis is conducted to demonstrate the validity and applicability of the suggested approaches compared to existing methods. [ABSTRACT FROM AUTHOR]

In this paper, we prove some Banach fixed point theorems in generalized metric space where the contractive conditions are endowed with the Hadamard product of real symmetric positive definite matrices. Since the condition that a matrix A converges to zero is not needed, this produces stronger results than those of Perov. As an application of our results, we study the existence and uniqueness of the solution for a system of matrix equations. [ABSTRACT FROM AUTHOR]

In this article, we present the study of μ -fuzzy subgroups and prove numerous fundamental algebraic attributes of this newly defined notion. We also define the concept of μ -fuzzy normal subgroup and investigate many vital algebraic characteristics of these phenomena. In addition, we characterize the quotient group induced by this particular fuzzy normal subgroup and establish a group isomorphism between the quotient groups G / κ μ and G / κ ∗ μ . Furthermore, we initiate the study of level subgroup, open level subgroup, and tangible subgroup of a μ -fuzzy subgroup and emphasize the significance of μ -fuzzy normal subgroups by establishing a relationship between these newly defined notions and μ -fuzzy normal subgroup. [ABSTRACT FROM AUTHOR]