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The power-law nanofluid's heat and mass transmission over a stretched surface with magnetic field, entropy optimization, and chemical reaction effects is the main focus of the present study. The governing partial differential equations are reduced using similarity transformation into ODEs (ordinary differential equations), which are then numerically solved with the help of the Keller box and finite difference techniques. A substantial evaluation is conducted using the controlling flow factors, which include the Eckert number, chemical reaction factor, Brownian motion parameter, thermophoresis number, power-law index (n), and generalized Prandtl number (Pr), on the fluid velocity profile, flowing fluid temperature, and concentration profile. A decrease in the velocity profile is observed when the chemical reaction process is accelerated, leading to heat absorption. However, when the power-law parameter increases, the fluid's temperature decreases, and the velocity profile increases at specific values of viscous dissipation (Ec = 0.1) and chemical reaction (γ = 0.01). The values of the coefficient of skin friction (Cf), Sherwood factor (Shx), and reduced local Nusselt number ( N u x are also computed and presented in the form of a table for the generalized Prandtl number (Pr = 7.0). The coefficient of skin friction and mass transfer and heat transfer rates are quantitatively compared with those in the literature for particular circumstances, and the results demonstrate good agreement with each other. This research offers insightful information for designing and improving systems that use nanofluids exposed to external magnetic fields, which has ramifications in many technical uses, including heat exchange systems based on nanofluids and thermal management systems. [ABSTRACT FROM AUTHOR]

In this work, we consider the degenerate Frobenius-Euler-Genocchi polynomials utilizing the degenerate exponential function and the degenerate Changhee-Frobenius-Euler-Genocchi polynomials utilizing the degenerate logarithm function. Then, we analyze some summation and addition formulas for these polynomials. In addition, we derive some correlations with degenerate Stirling numbers of both kinds and degenerate Frobenius-Euler polynomials. Moreover, we present difference and derivative operator rules for the generalized degenerate Frobenius-Euler-Genocchi polynomials. Lastly, we show certain zeros of both the degenerate Frobenius-Euler-Genocchi polynomials and the degenerate Changhee-Frobenius-Euler-Genocchi polynomials and provide their beautifully graphical representations. [ABSTRACT FROM AUTHOR]

This study presents a piecewise non-linear binary subdivision scheme based on a four-point linear binary subdivision scheme. This scheme is first transformed into a piecewise linear subdivision scheme and then into a piecewise non-linear subdivision scheme. The non-linear subdivision approach removes artifacts and distortions from limit curves, producing better continuous curves. The study demonstrates that this technique is a workable technique for producing smooth curves, especially when avoiding bends, distortion, and oscillation. [ABSTRACT FROM AUTHOR]

Special functions and special polynomials have been used and studied widely in the context of Geometric function theory of Complex Analysis by the many authors. Here, in our present investigations, making use of the convolution, we first introduce a new subclass of Bazilevivč bi-univalent functions involving the Bernoulli Polynomials. We then find the first two Taylor-Maclaurin coefficient | a 2 | and | a 3 | for our defined functions class. We then calculate the bounds for the Fekete Szegö inequality for the defined function class. Also some known consequences of our main results are highlighted in the form of Corollaries. [ABSTRACT FROM AUTHOR]

In this paper, we present two collocation methods utilizing subdivision schemes and Bernstein polynomials as their basis functions to solve Caputo-type fractional differential equations. These methods transform fractional differential equations into systems of linear equations, which can be solved using various suitable techniques. Notably, these methods are versatile, making them applicable to both boundary value problems and initial value problems. To demonstrate their effectiveness, we applied these methods to three test problems of fractional differential equations, including the Bagley-Torvik equation and fractional oscillation equation. Our results reveal that both methods provide a more accurate approximation to the exact solution when compared to various algorithms found in the existing literature, showcasing their efficiency, accuracy, and consistency. [ABSTRACT FROM AUTHOR]

The scourge of water pollution due to organic matter is a well-known fact. In order to address this issue, we employed a highly facile method of solid state reaction for the synthesis of bismuth potassium titanate, Bi0.5K0.5TiO3 (BKT) photocatalyst. Furthermore, the bandgap tailoring of the BKT is performed by photo-reduction of Ag onto the BKT, which results in the formation of hetero-structure junctions at the surface of the BKT. The as-prepared BKT and BKT-Ag photocatalysts are systematically characterized by x-ray diffraction, scanning electron microscopy, and high resolution transmission electron spectroscopy. Furthermore, the photocatalyst activity of the BKT and BKT-Ag was analyzed against the target organic pollutants by using UV–Vis spectroscopy. Three organic dyes such as methylene blue, eriochrome Black T, and methylene orange (MO) were used as target organic pollutants. The anchoring of Ag for the formation of hetero-structure junctions at the surface of BKT rendered it to be an ideal photo-catalyst with a bandgap reduction from 3.37 to 2.08 eV. Therefore, lowering the bandgap resulted in enhanced photocatalytic activity of the BKT-Ag. Among the three target dyes, BKT-Ag showed remarkable photo-degradation of MO and Erb T by degrading ≥90% of MO and Erb T in 120 min at neutral pH values. It is believed that BKT based photocatalysts can provide a unique platform for the removal of organic pollutants from wastewater. [ABSTRACT FROM AUTHOR]

In this paper, we propose a numerical scheme to solve generalized space fractional partial differential equations (GFPDEs). Besides, the proposed GFPDEs represent a great generalization of a significant type of FPDEs and their applications, which contain many previous reports as a special case. Moreover, the proposed scheme uses shifted Chebyshev sixth-kind (SCSK) polynomials with spectral collocation approach. The fractional differential derivatives are expressed in terms of the Caputo's definition. Furthermore, the Chebyshev collocation method together with the finite difference method is used to reduce these types of differential equations to a system of algebraic equations which can be solved numerically. In addition, the classical fourth-order Runge-Kotta method is also used to treat the differential system with the collocation method which obtains a great accuracy. Numerical approximations performed by the proposed method are presented and compared with the results obtained by other numerical methods. The introduced numerical experiments are fractional-order mathematical physics models, as advection-dispersion equation (FADE) and diffusion equation (FDE). The results reveal that our method is a simple and effective numerical method.

Various integral representations of hypergeometric functions have been introduced and investigated due to their important applications in divers fields. In this article, we define some new Euler-type integral representations for the Horn's functions of two variables G1, G2, G3 and H1.

The theme of this study is to investigate the theoretical and numerical simulation of heat and mass transfer of magneto hydrodynamic power-law nanofluid flow over a stretching sheet with surface heat flux and Soret/Dufour effects. The mass flux and energy flux increase with temperature and concentration differences using the Soret/Dufour impact. The similarity transformations were used to transform a physical problem into a non-linear differential equation, and the non-linear equations were solved by the Keller box technique. The Soret/Dufour and magnetic field are incorporated into a nanofluid model. The similarity transformation was used to reduce thermal energy, mass, and momentum in algebraic systems. The impact of nanofluid factors, such as generalized Brownian motion parameter Nb, Dufour parameter Df, Soret parameter Sr, Le, and Pr, are generalized Lewis and Prandtl numbers; the thermophoresis parameter Nt and magnetic parameter on dimensionless stretching surface functions are shown numerically and graphically. The quantitative relationship between heat transfer and skin friction is shown by using Keller box and MATLAB. The skin friction coefficient Cf, Sherwood number Shx, and Nusselt number Nux values were also computed and displayed on the graph. The increment in slip temperature, fluid velocity, and fluid concentration is enhanced with a high Dufour parameter. The temperature variation and fluid concentration are decreased with applied-magnetic effects because the magnetic field acts like an insulating material in heat transfer systems. The enhancement in the Nusselt number and Sherwood number is increased with Soret and Dufour effects. [ABSTRACT FROM AUTHOR]

In this paper, we introduce ten new quadruple hypergeometric series. We also obtain their various properties such that integral representations, fractional derivatives, N-fractional connections, operational relations and generating functions. [ABSTRACT FROM AUTHOR]

The theory of mixed fractional operators is still an uncovered area in fractional modelling. These multi-sided operators result by combining two fractional derivatives with different kernels, that is, the right-sided Caputo's and the left-sided Riemann-Liouville's fractional operators in a sequential manner. Although it may capture different memory phenomenons, there is no general approach to approximate the solution of the mixed type fractional differential equations (MFDEs). In this article, the authors introduce a novel numerical technique that relies on obtaining the matrix representation of the mixed operators. This was done by considering a new extension of the shifted Chebyshev polynomials of the fifth-kind (SFCPs) with a variable domain as a basis of L2 space. Then we employ the spectral collocation method together with the operational matrix to transform the MFDE into the corresponding system of algebraic equations. The convergence analysis of the proposed technique was studied in terms of the generalized Taylor's formula and the Gram determinant. Our findings facilitate further development of this theory by providing such a method of approximation. [ABSTRACT FROM AUTHOR]

This paper introduces a modified method for construction of a new design-control 6-point approximating refinement scheme. The construction of the new scheme is based on translation of the points of 4-point approximating refinement scheme to the new position according to the linear combination of certain displacement vectors. The initial and terminal points of these vectors are the refinement points of two 4-point approximating binary schemes. The new scheme contains three design-control parameters. These parameters increase the efficiency and flexibility of the new scheme. The mathematical and graphical analysis of the refinement scheme show that this scheme is good choice for curve modeling. [ABSTRACT FROM AUTHOR]