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The unsteady flow of Williamson fluid with the effect of bioconvection in the heat and mass transfer occurring over a stretching sheet is investigated. A uniform magnetic field, thermal radiation, thermal dissipation, and chemical reactions are taken into account as additional effects. The physical problem is formulated in the form of a system of partial differential equations and solved numerically. For this purpose, similarity functions are involved to transmute these equations into corresponding ordinary differential equations. After that, the Runge-Kutta method with shooting technique is employed to evaluate the desired findings with the utilization of a MATLAB script. As a result, the effects of various physical parameters on the velocity, temperature, and nanoparticle concentration profiles as well as on the skin friction coefficient and rate of heat transfer are discussed with the aid of graphs and tables. The parameters of Brownian motion and thermophoresis are responsible for the rise in temperature and bioconvection Rayleigh number diminishes the velocity field. This study on nanofluid bioconvection has been directly applied in the pharmaceutical industry, microfluidic technology, microbial improved oil recovery, modelling oil and gas-bearing sedimentary basins, and many other fields. Further, to check the accuracy and validation of the present results, satisfactory concurrence is observed with the existing literature.

The intuitionistic fuzzy hypersoft set (IFHSS) is the most generalized form of the intuitionistic fuzzy soft set used to resolve uncertain and vague data in the decision-making process, considering the parameters’ multi-sub-attributes. Aggregation operators execute a dynamic role in assessing the two prospect sequences and eliminating anxieties from this perception. This paper prolongs the IFHSS to interval-valued IFHSS (IVIFHSS), which proficiently contracts with hesitant and unclear data. It is the most potent technique for incorporating insecure data into decision-making (DM). The main objective of this research is to develop the algebraic operational laws for IVIFHSS. Furthermore, using the algebraic operational law, some aggregation operators (AOs) for IVIFHSS have been presented, such as interval-valued intuitionistic fuzzy hypersoft weighted average (IVIFHSWA) and interval-valued intuitionistic fuzzy hypersoft weighted geometric (IVIFHSWG) operators with their essential properties. Multi-criteria group decision-making (MCGDM) technique is vigorous for material selection. However, conventional methods of MCGDM regularly provide inconsistent results. Based on the expected AOs, industrial enterprises propose a robust MCGDM material selection method to meet this shortfall. The real-world application of the planned MCGDM method for cryogenic storing vessel material selection (MS) is presented. The implication is that the designed model is more efficient and consistent in handling information based on IVIFHSS.

In this paper, we introduce the notion of tricomplex valued metric space and prove some common fixed point theorems. The presented results generalize and expand some of the literature well-known results. We also explore some applications of our key results.

Complex Urysohn integral equations and complex Fredholm integral equation of the second kind have intensified the attention of appreciable researchers to their solution due to their comprehensive applications. This study is devoted to the existence and uniqueness of solution to these integral equations in the setting of complete complex double controlled metric spaces via fixed point theory. For this motive, a fixed point result together with a numerical example for the convergence behavior of operator to the fixed point is analyzed in the context of the quoted metric spaces.

Enhancement of heat transfer due to stretching sheets can be appropriately controlled by the movement of the nanofluids. The concentration and settling of the nanoparticles in the viscous MHD fluid and bioconvection are addressed. In this scenario, the fluid flow occurring in the presence of a normal and uniform magnetic field, thermal radiation, and chemical reaction is taken into account. For the two-dimensional flow with heat and mass transfer, five dependent variables and three independent variables constitute the system of partial differential equations. For this purpose, similarity functions are involved to convert these equations to corresponding ODEs. Then, the Runge–Kutta method with shooting technique is used to evaluate the required findings with the utilization of MATLAB script. The fluid velocity becomes slow against the strength of the magnetic parameter. The temperature rises with the parameter of Brownian motion and thermophoresis. The bioconvection Lewis number diminishes the velocity field. Compared with the existing literature, the results show satisfactory congruences.

In this work, a comprehensive study of fluid forces and thermal analysis of two-dimensional, laminar, and incompressible complex (power law, Bingham, and Herschel–Bulkley) fluid flow over a topological cross-sectional cylinder (square, hexagon, and circle) in channel have been computationally done by using finite element technique. The characteristics of nonlinear flow for varying ranges of power law index 0.4 ≤ n ≤ 1.6 , Bingham number 0 ≤ Bn ≤ 50 , Prandtl number 0.7 ≤ Pr ≤ 10 , Reynolds number 10 ≤ Re ≤ 50 , and Grashof number 1 ≤ Gr ≤ 10 have been examined. Considerable evaluation for thermal flow field in the form of dimensionless velocity profile, isotherms, drag and lift coefficients, and average Nusselt number Nu avg is done. Also, for a range of Bn , the drag forces reduction is observed for circular and hexagonal obstacles in comparison with the square cylinder. At Bn = 0 corresponding to Newtonian fluid, maximum reduction in drag force is reported.

It is considered that there is a fascinating issue in theoretical chemistry to predict the physicochemical and structural properties of the chemical compounds in the molecular graphs. These properties of chemical compounds (boiling points, melting points, molar refraction, acentric factor, octanol-water partition coefficient, and motor octane number) are modeled by topological indices which are more applicable and well-used graph-theoretic tools for the studies of quantitative structure-property relationships (QSPRs) and quantitative structure-activity relationships (QSARs) in the subject of cheminformatics. The π -electron energy of a molecular graph was calculated by adding squares of degrees (valencies) of its vertices (nodes). This computational result, afterwards, was named the first Zagreb index, and in the field of molecular graph theory, it turned out to be a well-swotted topological index. In 2011, Vukicevic introduced the variable sum exdeg index which is famous for predicting the octanol-water partition coefficient of certain chemical compounds such as octane isomers, polyaromatic hydrocarbons (PAH), polychlorobiphenyls (PCB), and phenethylamines (Phenet). In this paper, we characterized the conjugated trees and conjugated unicyclic graphs for variable sum exdeg index in different intervals of real numbers. We also investigated the maximum value of SEIa for bicyclic graphs depending on a > 1 .

With the study of extensive literature on the Laplace transform with one and two variables and its properties, applications are available, but there is no work on n-dimensional Laplace transform. In this research article, we define n-dimensional fractional frequency Laplace transform with shift values. Several theorems are derived with properties of the Laplace transform. The results are numerically analyzed and discussed through MATLAB.

In many flow phenomenons of fluid with medium molecular weight, the energy flux is effected due to the inhomogeneity of concentration of mass. This contribution of the concentration to the energy flux is considered as diffusion-thermo effect or Dufour effect. In this research article the diffusion-thermo effect is addressed for the magnetohydrodynamics (MHD) flow of Jeffrey’s fractional fluid past an exponentially accelerated vertical plate with generalized thermal and mass transports through a porous medium. For the generalization of the thermal and mass fluxes the constant proportional Caputo (CPC) fractional derivative is utilized. The governing of this generalized flow are reduced to non-dimensional forms and then solved semi analytically by Laplace transform. In additions the physical aspects of flow and material parameters especially the effect of D u and fractional parameters are discussed by sketching the graphs. From the graphical illustration, it is concluded that in the presence of Dufour effect flow speeds up. Moreover, a comparison between fractionalized and ordinary velocity fields is also drawn and it is also observed that fractional model with constant proportional derivative is of the more decaying nature as compare to the model contracted with classical Caputo and Caputo fractional derivatives.

Because of its influence on various elements of human life experiences and conditions, the building industry is a significant business. In the recent past, environmental considerations have been incorporated in the design and planning stages of building supply chains. The process of evaluating and selecting suppliers is one of the most important issues in supply chain management. A multicriteria decision-making (MCDM) problem can be utilized to handle such issues. The goal of this research is to present a new and efficient technique for selecting suppliers with ambiguous data. The suggested methodology’s structure is based on technology for order of preference by similarity to ideal solution (TOPSIS), with Fermatean fuzzy sets ( F r FSs) employed to cope with information uncertainty. In this article, authors modified the distance between F r FSs to propose the similarity measure and implemented it to form the MCDM model to resolve the vague and uncertain data. Moreover, we used this similarity measure to choose the optimal alternative. A practical example for alternative selection is provided, along with a comparison of the acquired findings to existing approach. Finally, to strengthen the outcome obtained through the proposed model, sensitivity analysis and time complexity analysis are performed.

In this paper, we examine the multicriteria decision-making (MCDM) difficulties for Pythagorean fuzzy hypersoft sets (PFHSSs). The PFHSSs are a suitable extension of the Pythagorean fuzzy soft sets (PFSSs) which deliberates the parametrization of multi-subattributes of considered parameters. It is a most substantial notion for describing fuzzy information in the decision-making (DM) procedure to accommodate more vagueness comparative to existing PFSSs and intuitionistic fuzzy hypersoft sets (IFHSSs). The core objective of this study is to plan some innovative operational laws considering the interaction for Pythagorean fuzzy hypersoft numbers (PFHSNs). Also, based on settled interaction operational laws, two aggregation operators (AOs) i.e., Pythagorean fuzzy hypersoft interaction weighted average (PFHSIWA) and Pythagorean fuzzy hypersoft interaction weighted geometric (PFHSIWG) operators for PFHSSs operators have been presented with their fundamental properties. Furthermore, an MCDM technique has been established using planned interaction AOs. To ensure the strength and practicality of the developed MCDM method, a mathematical illustration has been presented. The usefulness, influence, and versatility of the developed method have been demonstrated via comparative analysis with the help of some conventional studies.

This paper is related to frame a mathematical analysis of impulsive fractional order differential equations (IFODEs) under nonlocal Caputo fractional boundary conditions (NCFBCs). By using fixed point theorems of Schaefer and Banach, we analyze the existence and uniqueness results for the considered problem. Furthermore, we utilize the theory of stability for presenting Hyers-Ulam, generalized Hyers-Ulam, Hyers-Ulam-Rassias, and generalized Hyers-Ulam-Rassias stability results of the proposed scheme. Finally, some applications are offered to demonstrate the concept and results. The whole analysis is carried out by using Caputo fractional derivatives (CFDs).

In this article, we consider the analytic solutions of the uncertain fractional backward difference equations in the sense of Riemann–Liouville fractional operators which are solved by using the Picard successive iteration method. Also, we consider the existence and uniqueness theorem of the solution to an uncertain fractional backward difference equation via the Banach contraction fixed-point theorem under the conditions of Lipschitz constant and linear combination growth. Finally, we point out some examples to confirm the validity of the existence and uniqueness of the solution.

This study reveals new fractional behavior of Minkowski inequality and several other related generalizations in the frame of the newly proposed fractional operators. For this, an efficient technique called generalized proportional fractional integral operator with respect to another function Φ is introduced. This strategy usually arises as a description of the exponential functions in their kernels in terms of another function Φ. The prime purpose of this study is to provide a new fractional technique, which need not use small parameters for finding the approximate solution of fractional coupled systems and eliminate linearization and unrealistic factors. Numerical results represent that the proposed technique is efficient, reliable, and easy to use for a large variety of physical systems. This study shows that a more general proportional fractional operator is very accurate and effective for analysis of the nonlinear behavior of boundary value problems. This study also states that our findings are more convenient and efficient than other available results.