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In this study, we define new class of holomorphic functions associated with tangent function. Furthermore, we examine the differential subordination implementation results related to Janowski and tangent functions. Also, we investigate some extreme point theorem and partial sums results, necessary and sufficient conditions, convex combination, closure theorem, growth and distortion bounds, and radii of close-to-starlikeness and starlikeness for this newly defined functions class of holomorphic functions.

Due to the absence of a negative of three membership functions, there are drawbacks to the existing definition of a picture fuzzy graph (PFG). In that definition of bipolar picture fuzzy graph (BPFG), membership function, neutral membership function, nonmembership function, negative of membership function, negative of neutral membership function, and negative of nonmembership function are involved. A BPFG is the extension of PFG. In this manuscript, we present some properties of symmetric difference, and rejection of BPFG.

In this article, first integral method (FIM) is used to acquire the analytical solutions of (3+1)-D Wazwaz–Benjamin–Bona–Mahony and (2+1)-D cubic Klein–Gordon equation. New soliton solutions are obtained, such as solitons, cuspon, and periodic solutions. FIM is a direct method to acquire soliton solutions of nonlinear partial differential equations (PDEs). The proposed technique can be used for solving higher dimensional PDEs. FIM can be implemented to solve integrable and ion-integrable equations.

Generally, fractional partial integro-differential equations (FPIDEs) play a vital role in modeling various complex phenomena. Because of the several applications of FPIDEs in applied sciences, mathematicians have taken a keen interest in developing and utilizing the various techniques for its solutions. In this context, the exact and analytical solutions are not very easy to investigate the solution of FPIDEs. In this article, a novel analytical approach that is known as the Laplace adomian decomposition method is implemented to calculate the solutions of FPIDEs. We obtain the approximate solution of the nonlinear FPIDEs. The results are discussed using graphs and tables. The graphs and tables have shown the greater accuracy of the suggested method compared to the extended cubic-B splice method. The accuracy of the suggested method is higher at all fractional orders of the derivatives. A sufficient degree of accuracy is achieved with fewer calculations with a simple procedure. The presented method requires no parametrization or discretization and, therefore, can be extended for the solutions of other nonlinear FPIDEs and their systems.

Usually, to find the analytical and numerical solution of the boundary value problems of fractional partial differential equations is not an easy task; however, the researchers devoted their sincere attempt to find the solutions of various equations by using either analytical or numerical procedures. In this article, a very accurate and prominent method is developed to find the analytical solution of hyperbolic-telegraph equations with initial and boundary conditions within the Caputo operator, which has very simple calculations. This method is called a new technique of Adomian decomposition method. The obtained results are described by plots to confirm the accuracy of the suggested technique. Plots are drawn for both fractional and integer order solutions to confirm the accuracy and validity of the proposed method. Solutions are obtained at different fractional orders to discuss the useful dynamics of the targeted problems. Moreover, the suggested technique has provided the highest accuracy with a small number of calculations. The suggested technique gives results in the form of a series of solutions with easily computable and convergent components. The method is simple and straightforward and therefore preferred for the solutions of other problems with both initial and boundary conditions.

In this paper, the extended tanh and hirota methods are used to construct soliton solutions for the WuZhang (WZ) system. Singular solitary wave, periodic and multi soliton solutions of the WZ system are obtained.

In this manuscript we investigate electrodynamic flow. For several values of the intimate parameters we proved that the approximate solution depends on a reproducing kernel model. Obtained results prove that the reproducing kernel method (RKM) is very effective. We obtain good results without any transformation or discretization. Numerical experiments on test examples show that our proposed schemes are of high accuracy and strongly support the theoretical results.

The development and stability of acoustic thin-shell wormholes (WHs) within the context of acoustic black holes are examined in this paper. Utilizing linearized radial perturbations, the stability of these WHs is examined. In this study, a variety of equations of state are taken into account, including barotropic, variable Chaplygin, and phantom-like equations of state. According to the findings, the acoustic black hole structure has an unstable configuration for barotropic fluid. However, as the parameter ℰ gets closer to zero, it does not show any stable or unstable configurations at the event horizon position. For higher values of n and ξ , the resulting structure for the phantom-like variable equation of state (EoS) displays stable behavior away from the horizon while presenting unstable configurations close to the event horizon. The possibility of a stable structure rises as n is increased. Additionally, the constructed structure exhibits stable behavior for n = 1 under extreme acoustic black holes, whereas thin-shell topologies demonstrate unstable behavior outside the event horizon for the generalized Chaplygin variable EoS. However, the structure stabilizes for n = 1 at higher values of ξ. The stability of acoustic thin-shell WHs is higher than that of Schwarzschild thin-shell WHs for smaller values of n , indicating that the acoustic black hole parameter greatly influences the stable configurations of thin-shell WHs. [ABSTRACT FROM AUTHOR]

Boron, the element which is in close proximity with carbon in the periodic table has been hypothesized to produce diverse two‐dimensional structures that differ from well‐studied 2D materials. Icosahedron B12$$ {\mathcal{B}}_{12} $$, the monomers of which form the crystalline boron structure, appears as a recurring pattern in the chemistry of boron compounds, elemental boron and boron‐rich materials, functions as a building block in a majority of boron allotropes. The topological study of the icosahedral sheets is a necessary field to be investigated for the effective analysis and characterization of its physico‐chemical attributes without undertaking time‐consuming experimental research. The topological descriptors being expressed as numerical values enable scientists to compare and correlate data, which can be applied to quantitative structure‐activity relationships and quantitative structure‐property relationships modeling. In this study, various degree based molecular descriptors of the crystal boron icosahedral α$$ \alpha $$ sheet Bα(a,b)$$ {\mathcal{B}}_{\alpha}\left(\mathfrak{a},\mathfrak{b}\right) $$ has been formulated from a two‐dimensional lattice perspective using the 필‐polynomial approach. To establish the significance of these descriptors in the study of chemical attributes, an efficient linear regression modeling has also been performed, enabling the prediction of properties of several other boron sheets. [ABSTRACT FROM AUTHOR]

Dendrimers recently emerged as a strong category of nanoparticles in the realm of nanomedicine due to their distinct structural properties. In order to bring the medications to mark the carrier vehicle, a specific design with the right qualities (topological invariants) might be targeted using the physical chemistry of dendrimers. Topological descriptors of chemical networks are numeric numbers that allow us to obtain information about a compound's structure and expose its underlying properties without the requirement for validation. In this work, we have computed the atom-bond connectivity index (ABC) and the atom-bond sum-connectivity index (ABS) of bismuth(III) iodide and PETAA dendrimer. A graphical comparison is given at the end to study the behavior of these two topological indices for bismuth (III) iodide and PETAA dendrimer. [ABSTRACT FROM AUTHOR]

For a simple, finite, and connected graph G, the spherical maximal operator is defined as ... where ... is the sphere with center at t and having radius r. In this paper, we consider the spherical maximal operator ... on ... spaces and calculate the ... for ... and estimate the ... for ..., when G is Km. Furthermore, We establish the maximum and minimum bounds for the spherical maximum operator on finite graphs and indicate the graphs that achieve these bounds. [ABSTRACT FROM AUTHOR]

In this work, we study some new applications of symmetric quantum calculus in the field of Geometric Function Theory. We use the cardioid domain and the symmetric quantum difference operator to generate new classes of multivalent q-starlike and q-convex functions. We examine a wide range of interesting properties for functions that can be classified into these newly defined classes, such as estimates for the bounds for the first two coefficients, Fekete–Szego-type functional and coefficient inequalities. All the results found in this research are sharp. A number of well-known corollaries are additionally taken into consideration to show how the findings of this research relate to those of earlier studies. [ABSTRACT FROM AUTHOR]

The aim of this investigation is to arrange partial differential equations (PDEs) into simplified form for gradients (mass and thermal) in the inclined magneto hydrodynamic flow of hybrid (CuO–TiO2/Water) nanoliquid in a permeable media. The modeled term is extremely nonlinear with the boundary conditions. So, this research focuses on numerical solution by using bvp4c solver in MATLAB software and by applying similarity transformation. Simulations have been done to discover the dynamics of stream and the transport of heat and mass under parametric deviation. To examine the impact of a temperature gradient on the transport of mass and the role of a concentration gradient on the transport of heat energy, outcomes have been documented in tabular form and shown through graphs. Remarkable changes in motion, temperature and concentration are noted when Dufour and Soret numbers vary. [ABSTRACT FROM AUTHOR]

The investigation of heat and mass transfer between two porous disks containing porous media is the focus of this paper. In this research, (Ag–Al2O3/water)-based hybrid nanofluid is used. Governing partial differential equations are converted to nonlinear ordinary differential equations by similarity transformations. Numerical solutions to nonlinear systems of equations are achieved using the shooting technique. It is examined how the particle's diameter and nanolayer thickness affect the thermal conductivity of a hybrid nanofluid. Due to the increment of nanolayer thickness, the Nusselt number increases and vice versa for the radius of the particle. Tables and graphs show how the governing parameters influence velocity, temperature, and mass concentration profiles, as well as physical quantities such as skin friction coefficient and Nusselt number. As the values of the porous medium parameters ( P m = 7 –13) and nanolayer thickness (h = 4 –12) elevate, the flow of skin friction coefficient and Nusselt number escalate in both porous disks. Moreover, as the values of the particle radius (r = 9 % to 12%) and Reynolds number (Re = − 1 to 2) amplify, the flow of heat transfer rate is diminished in the lower disk. Porous materials have a high surface area, which increases the contact area between the nanofluids and the porous medium. Porous materials can enhance the permeability of the fluid, reducing the pressure drop in the system. This can be advantageous in applications where high flow rates and low-pressure drops are desired, such as in heat exchangers or cooling systems. Porous materials can provide trapping sites or adhesion points for the nanoparticles, enhancing their dispersion and stability within the hybrid nanofluids. The porosity of the flow medium can therefore influence the purification and filtration efficiency of the hybrid nanofluids, ensuring their cleanliness and functionality. Understanding and controlling the porosity can help optimize the flow characteristics of the nanofluids in various applications. Overall this field will focus on refining hybrid nanofluid compositions, improving modeling techniques, validating experimental findings, optimizing system designs, and exploring new applications. [ABSTRACT FROM AUTHOR]