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Abstract The current study examines the numerical simulation of the nanoliquid boundary layer flow comprising gyrotactic microbes with mass and energy transmission across a stretching inclined cylinder. The consequences of chemical reaction, heat generation/absorption, buoyancy force and Arrhenius activation energy is also considered on the nanofluid flow. The flow mechanism has been modeled in the form of system of nonlinear partial differential equations (PDEs). That system of PDEs is further transform into the dimensionless set of ordinary differential equations (ODEs) through the similarity substitutions. The obtained set of differential equations are numerically computed through the parametric continuation method (PCM). The effects of the distinct physical constraints on the energy, velocity, mass and the motile microbe profiles are discoursed and evaluated through Tables and Figures. It has been noticed that the velocity curve drops with the influence of inclination angle and Richardson number, while enhances against the variation of curvature factor. Furthermore, the energy field boosts with the upshot of inclination angle and heat source term, while declines with the influence of Prandtl number and Richardson number.

In recent years, numerous scholars have investigated the relationship between symmetry and generalized convexity. Due to this close relationship, generalized convexity and symmetry have become new areas of study in the field of inequalities. With the help of fuzzy up and down relation, the class of up and down λ-convex fuzzy-number valued mappings is introduced in this study; and weighted Hermite-Hadamard type fuzzy inclusions are demonstrated for these functions. The product of two up and down λ-convex fuzzy-number valued mappings also has Hermite-Hadamard type fuzzy inclusions, which is another development. Additionally, by imposing some mild restrictions on up and down λ-convex (λ-concave) fuzzy number valued mappings, we have introduced two new significant classes of fuzzy number valued up and down λ-convexity (λ-concavity), referred to as lower up and down λ-convex (lower up and down λ-concave) and upper up and down λ-convex (λ-concave) fuzzy number valued mappings. Using these definitions, we have amassed many classical and novel exceptional cases that implement the key findings. Our proven results expand and generalize several previous findings in the literature body. Additionally, we offer appropriate examples to corroborate our theoretical findings.

Monkeypox (MPX) is a global public health concern. This infectious disease affects people all over the world, not just those in West and Central Africa. Various approaches have been used to study epidemiology, the source of infection, and patterns of transmission of MPX. In this article, we analyze the dynamics of MPX using a fractional mathematical model with a power law kernel. The human-to-animal transmission is considered in the model formulation. The fractional model is further reformulated via a generalized fractal-fractional differential operator in the Caputo sense. The basic mathematical including the existence and uniqueness of both fractional and fractal-fractional problems are provided using fixed points theorems. A numerical scheme for the proposed model is obtained using an efficient iterative method. Moreover, detailed simulation results are shown for different fractional orders in the first stage. Finally, a number of graphical results of fractal-fractional MPX transmission models are presented showing the combined effect of fractal and fractional orders on model dynamics. The resulting simulations conclude that the new fractal-fractional operator added more biological insight into the dynamics of illness.

A curved enclosure in attendance of MHD was evaluated in this article. Both outer cold and inner hot surfaces have curved shapes which boosts the convective rate. The impact of MHD in equations has been applied and there is one negative term is x direction if horizontal magnetic fields have been applied. Presence of such a field leads to generation of Lorentz force which prevents the nanofluid from moving faster. Such reduction in velocity with growth of Ha makes Nu decrease. Adding nanoparticles with greater “m” and φ can increase the convective flow. When Ra = 700, dispersing nano-powders can enhance the Nu in existence of MHD about 41.9%. When Ra = 150, Nu can improve about 12.01% if “m” is enhanced. Nu decreases around 40.1% with growth of Ha while it increases about 43.36% in existence of greater Ra.

We introduce a topology on the set of vertices of a directed graph and we call the topological space as pathless directed topological space. We study relation between the relative topologies and pathless directed topological spaces of E-generated subdirected graphs. Then, we study connectedness, isomorphic and homeomorphic properties in digraphs and pathless directed topological spaces. Moreover, we apply our results to blood circulation process in human heart and disprove Shokry and Aly [M. Shokry and R. E. Aly, Topological properties on graph vs medical application in human heart, Int. J. Appl. Math., 15 (2013), 1103-1109], Nada et al. [S. Nada, A. E. F. El Atik and M. Atef, New types of topological structures via graphs, Math. Method. Appl. Sci., 41 (2018), 5801-5810] and Nawar et al. [A. S. Nawar and A. E. F. A. El-Atik, A model of a human heart via graph nano topological spaces, Int. J. Biomath., 12 (2019), p.1950006]. We show that pathless directed topology is accurately describing the circulation of blood in the heart of human body.

The current article aims to simulate the promising influence of porous zones on treatment of working fluid within curved shaped containers under the impact of MHD. The MHD was applied in x direction which produces one negative source term in the y velocity equation. The features of base fluid have been improved with dispersing Al2O3 nanoparticles. The formulation based on Ψ was used to simplify the equations and finally the equations were solved via CVFEM. Results showed that dispersing nano-powders boost the convective rate about 39.34% in the presence of MHD. Increase in shape factor can make Nu increase about 11.46%. The applying MHD causes Nu to reduce about 54.93%. Augment of Ra makes Nu augments around 68.91%.

To evaluate the efficiency of a system involving wavy shapes of wall, numerical technique has been utilized in this article. The region between two wavy complex surfaces was fabricated from porous material and the working fluid is nanofluid (mixture of water with various shapes of alumina nanoparticles). The new terms related to porous media have been added according to Darcy law. The pressure terms were removed with defining stream function. The last form of equations contains two variables (θ and Ψ) which were solved via CVFEM. The results from the present code have been compared with previous article and good agreement was reported. With augmenting Ha, the speed of nanofluid decreases and Nu drops about 50.48% when Ra = 700. Considering greater buoyancy force makes Nu to increase about 61.36% when Ha = 0. The shape factor has a direct relation with the amount of conductivity, thus, Nu enhances about 11.97% with an increase of this factor when Ha = 15, Ra = 150.

The new computational approach has been incorporated for modeling the nanofluid flow through a cavity involving a wavy inner wall which experiences uniform flux. The fluid was created by loading alumina powders with various shapes within the water. The stream function formulation was applied after employing Darcy law and final equations have been generated. The container is under the impact of Lorentz force in addition to buoyancy forces. With loading additives, Nu enhances about 17.07% and 41.57% depending on the amount of Ha. The greater value of Ha makes the effect of adding nanoparticles become more sensible. With increasing the value of shape factor, Nu increases about 11.76%. As Ha grows, the rate of cooling decreases about 41.31%. With augment of Ra, Nu enhances about 50.41% in absence of Ha.

This article is devoted to showing the existence and uniqueness (EU) of a solution with non-Lipschitz coefficients (NLC) of fractional Itô-Doob stochastic differential equations driven by countably many Brownian motions (FIDSDECBMs) of order ϰ∈(0,1) by using the Picard iteration technique (PIT) and the semimartingale local time (SLT).

In this article, we discuss the existence and uniqueness of proportional Itô–Doob stochastic fractional order systems (PIDSFOS) by using the Picard iteration method. The paper provides new results using the proportional fractional integral and stochastic calculus techniques. We have shown the convergence of the solution of the averaged PIDSFOS to that of the standard PIDSFOS in the context of the mean square and also in probability. One example is given to illustrate our results.

Convex bodies are naturally symmetrical. There is also a correlation between the two variables of symmetry and convexity. Their use, in either case, has been feasible in recent years because of their interchangeable and similar properties. The proposed analysis provides information on a new class for a convex function which is known as up and down X1,X2-convex fuzzy-Number valued mappings (UD-X1,X2-convex FNVM). Using this class, we disclosed a number of new versions of integral inequalities. Additionally, we give a number of new related integral inequalities connected to the well-known Hermite-Hadamard-type inequalities. In conclusion, some examples are given to back up and show the value of these new results.

The topic of convex and nonconvex mapping has many applications in engineering and applied mathematics. The Aumann and fuzzy Aumann integrals are the most significant interval and fuzzy operators that allow the classical theory of integrals to be generalized. This paper considers the well-known fuzzy Hermite–Hadamard (HH) type and associated inequalities. With the help of fuzzy Aumann integrals and the newly introduced fuzzy number valued up and down convexity (UD-convexity), we increase this mileage even further. Additionally, with the help of definitions of lower UD-concave (lower UD-concave) and upper UD-convex (concave) fuzzy number valued mappings (FNVMs), we have gathered a sizable collection of both well-known and new extraordinary cases that act as applications of the main conclusions. We also offer a few examples of fuzzy number valued UD-convexity to further demonstrate the validity of the fuzzy inclusion relations presented in this study.

A new class of generalized fuzzy open sets in fuzzy topological space, called fuzzy sp-open sets, are introduced, and their properties are studied and the relationship between this new concept and other weaker forms of fuzzy open sets we discussed. Moreover, we introduce the fuzzy sp-continuous (resp., fuzzy sp-open) mapping and other stronger forms of sp-continuous (resp., fuzzy sp-open) mapping and establish their various characteristic properties. Finally, we study the relationships between all these mappings and other weaker forms of fuzzy continuous mapping and introduce fuzzy sp-connected. Counter examples are given to show the noncoincidence of these sets and mappings.