The goal of this manuscript is to examine the measurability of relative multifractal measures and their related dimensions.

For modeling real-world problems in mathematical form, we encounter uncertain and ambiguous quantities. In such situations, the efficient fuzzy set (FS) theory is employed to model these uncertain and ambiguous quantities in the form of fuzzy numbers (FNs). Since comparing FNs is essential in most optimization problems, we are compelled to utilize a suitable ranking method (RM). In this paper, the limitations of the RMs discussed in the literature are addressed, and a new revised approach for ranking various types of FNs is introduced. Additionally, it has been demonstrated that this innovative RM consistently ensures alignment among the rankings of fuzzy quantities and their associated representations. To illustrate the usages, advantages, and efficiency of the proposed method for ranking fuzzy numbers (RFN), we will present several examples, and several comparative examples are provided. Finally, in order to demonstrate the usage and applicability of our recommended RM, a practical application called the fuzzy 1-center problem is solved.

In the following work, we employ the modified decomposition method to obtain approximate solutions to random ordinary linear and nonlinear differential equations. We will introduce a fast technique for finding approximate solutions and demonstrate the effectiveness, speed, and accuracy of this method through examples, the obtained results, and the impact of the stochastic process (generation of a Wiener process on a computer) on the shape of the solution to differential equations.

The current work is concerned with studying the effective effects of temperature distribution and pressure gradient in the curved channel for non-Newtonian Walter’s - B fluid. A fluid moving through an asymmetric curved peristaltic channel out of the porous medium with variable viscosity and non-slippery conditions on a temperature distribution, pressure gradient, pressure rise, and concentration. The heat equation was formulated by including the term heat source. The equations governing momentum, energy, and concentration were simplified under long-wavelength constraints and small Reynolds number estimates. A mathematical expression for the nonlinear partial equations was determined analytically in terms of the axial and transverse coordinates and by the regular turbulence for small values of the viscosity parameter of the Reynolds model. The approximation was used to derive series solutions for the temperature distribution field, the pressure gradient field and the evolution of the pressure rise. Adding to the focus area and performing numerical calculations of the pressure rise field for each wavelength. Explaining the effect of the physical parameters in this model on the computational results and the mathematical program “MATHEMATICA”.

For every n-dimensional nilpotent Lie algebra L, let ℳ(L)be the Schur multiplier of L. Then we define t(L) by t(L) = 1/2(n2 – n) – dimℳ(L). We classify nilpotent Lie algebras L satisfying t(L) = 13.

The purpose of that study is to provide many ideas related to the fuzzy k-skew ( μ–ℑ̆) quasi binormal operator that is defined on fuzzy Hilbert space. Additionally, several significant properties of this operator are discussed, and certain theorems of operations concerning this concept have been provided.

The study investigates the application of the concept of the addition of a deep learning system to fractional calculus (FC) in order to accelerate and generalize the learning process. We propose a different form of neural network FGNN, Fractional Gradient Neural Network. In this network, the derivatives of fractional order are the gradient dynamics in control resulting in the optimisation being more fluid and the extraction of features being improved. The approach is a hybrid between the ease of use and memory capabilities of FC and the adaptation and data-driven capabilities of DL. The picture and signaling datasets experimental results indicate that these networks are more precise, more robust and less prone to overfitting as compared to standard networks. These findings indicate that FC is an excellent mathematical foundation to make next-generation deep learning models improved.

In the systems making decisions, this paper examines the ability of set theory and logic to be combined as building blocks to AI-driven thinking. It is revealed that modeling any complex decision problem become clear and structured through the formalization of the knowledge representation by sets and logical formulae. Application of propositional and predicate logic allows strong reasoning processes to arrive at good results and assist individuals to make good decisions. In this case we demonstrate how to construct decision-making systems in a manner that represents them as logical and set-based structures. This approach offers a systematic and scientifically valid approach to the development of decision-support systems that are effective, easy to comprehend, and straightforward.

This paper presents the way of integrating various mathematical structures into one system that will result in the improvement of academic knowledge and liberate more useful applications. The work establishes a single approach, which considers groups, rings, fields, modules, and lattices in an inclusive algebraic perspective by applying universal algebra and category theory. This can be seen as such that it is easier to map morphisms and representation theories that retain significant algebraic properties the same across structures. The proposed framework holds a great potential to improve such area as algebraic topology, cryptography, and quantum algebra through the provision of new ideas and simplification of the processes. The issues that may arise and how this unified theory can be extended in the future are also discussed.

The major aim of this work is to apply a technique, Elzaki transform (ET), which is an iterative analytical technique to achieve an approximate analytical solution for some applications of nonlinear differential equations. This technique depends on applying ET which has been used to break down the partial differential equation solution into an infinite number of components. Moreover, some illustrative examples are given and the results obtained indicate the proposed method’s accuracy, efficiency, and reliability. Results like this demonstrate how effective and efficient this method is in resolving problems of this kind. Therefore, using fractional differential equations as a model, our suggested approach can be used to analyze the solutions of a broad range of genuine issues that arise in the natural sciences and engineering.