Narrow Results

The new generalized hypergeometric function (Yang $𝕐$-function) described by the contour-type Mellin–Barnes integral representation serves as the inspiration for this study. The incomplete Yang $𝕐$-functions ${}^{\gamma }{𝕐}_{r,s}^{p,q}(z)$ and ${}^{\mathrm{\Gamma }}{𝕐}_{r,s}^{p,q}(z)$ that we shall introduce here are the appropriate extension of a class of $𝕐$-functions by merit of the gamma functions of incomplete type, $\gamma (\sigma ,x)$ and $\mathrm{\Gamma }(\sigma ,x)$. In this work, our objective is to study several remarkable characteristics of these newly introduced incomplete $𝕐$-functions viz; reduction formula, derivative, various integral transformations. Additionally, using these newly established incomplete functions, we formulate and solve a generalized fractional kinetic equation in terms of these incomplete $𝕐$-functions. Further, we also propose the incomplete $𝕎$-functions ${}^{\gamma }{𝕎}_{p,q}^{r,s}$ and ${}^{\mathrm{\Gamma }}{𝕎}_{p,q}^{r,s}$ corresponding to a new generalization of the $𝕐$-function.

The focus in this study is to examine the flow formation of Taylor–Couette (T–C) for some fluids exhibiting non-Newtonian properties in a region of cylindrical annulus due to the effect of imposed stresses on the periphery of the inner cylinder while the outer cylinder is hanging around inert. This tangential shear will be liable for the motion of the fluid through the annulus. It is very often when researchers in different fields like engineering, mathematics and physics come across the complexity that the given mathematical model cannot be solved in the existing space and requires to be transformed in the space in which it can be easily solved. Thus, transforms are being used as a key tool for solving many dominant problems in different fields. Many transformations have been introduced by researchers but for solving problems in this study, we will make use of Hankel transform and Laplace transform to obtain the velocity field and the corresponding shear stresses (SS) for the fractional Oldroyd-B fluid (O-B fluid). In the end, a graphical presentation is given for the comparison of the effect on fluid motion due to different parameters like fractional parameters, relaxation and retardation times.

Among several aspects, the one contributing towards the difficulty of groundwater quality evaluation is the large diversity of contamination sources. As contaminants comprising various compounds move from the soil to the water table, they will travel through several hydrologic zones. In constant unidirectional flow fields, a mathematical study of simultaneous adsorption and dispersion of a solute inside homogeneous and isotropic permeable media is described. The solute is adsorbed at a rate proportionate to its concentration in the dispersion systems, which are susceptible to input concentrations that fluctuate exponentially with time. The advection–dispersion equation (ADE) was solved numerically in this work to analyze the pollutants transport bearing in mind the coefficient of distribution and permeability by considering pollutant input concentrations. The solution is derived using the Laplace transform and Duhamel’s theorem with moving coordinates. For specified medium and fluid characteristics, mathematical methods are created to forecast the concentration of pollutants in adsorbing porous media.

The classical Hartmann flow problem is still interesting and novel due to its applications in MHD generators, plasma physics, power systems, etc. Owing to such importance in mind, this investigation explores the natural convection flow of viscous fluid following the Hartmann flow phenomenon due to a cylindrical tube. The heat transfer characteristics with diffusion phenomenon have been taken into consideration. The classical problem is further extended by countering the magnetic force impact. The fractional framework based on the Atangana–Baleanu (AB) and Caputo–Fabrizio (CF) is performed. The closed-form solutions are attained with Laplace as well as finite Hankel transforms. Further, the obtained results are stated as a combination of G-functions of Lorenzo and Hartley. The particular cases for the obtained simulations have been performed. The role of flow parameters governing the flow is graphically attributed.

In this paper, the malaria transmission (MT) model under control strategies is considered using the Liouville–Caputo fractional order (FO) derivatives with exponential decay law and power-law. For the solutions we are using an iterative technique involving Laplace transform. We examined the uniqueness and existence (UE) of the solutions by applying the fixed-point theory. Also, fractal–fractional operators that include power-law and exponential decay law are considered. Numerical results of the MT model are obtained for the particular values of the FO derivatives $\varsigma$ and $\rho$.

A novel mathematical model in hygrothermoelastic theory has developed to describe heat and moisture distribution in a nonsimple medium. The model incorporates non-Fourier and non-Fick laws using a single phase-lag model to establish a relation between hygrothermoelasticity and unstable conduction processes. The model is applied to an ellipse-shaped composite material subjected to humid-heat loading. The Laplace and Mathieu integral transform was employed to obtain an exact solution of linearly coupled partial differential equations in an elliptical coordinate system. The Gaver–Stehfest algorithm is utilized for the inversion of Laplace functions. Berger’s approximation equation was employed to simplify the calculation of significant deformations for elliptic plates. The model also provides quantitative results for the composition of T300/5208, which consists of epoxy resin reinforced with graphite fibers. The hygrothermal behaviors due to the single-phase-lag time, geometry dimensions, material type, and the two temperatures are explored. The results reveal that nonclassical theories with single-phase-lag time and two-temperature have significant influences on the hygrothermoelastic behaviors in elliptic-shaped objects. The investigation can be effectually led using micro- and nano-elliptic shape resonators in future research.

The present paper deals with the disturbances due to periodic strip thermal sources, acting on the rigidly fixed, charge free (open circuit) or electrically shorted (closed circuit) surface of a homogeneous, transversely isotropic, thermally conducting generalized piezothermoelastic half-space. The Laplace and Fourier transform technique have been employed to solve the model consisting of partial differential equations and boundary conditions in the transformed domain. In order to obtain the displacements, temperature change, stresses, electric potential and electric displacement in the physical domain, the integral transforms have been inverted by using a numerical inversion technique. Finally, to illustrate the analytical results, the numerical computations of various field parameters have been carried out from the relevant expressions and relations for cadmium selenide (CdSe) material by developing a FORTRAN code. The computer simulated results are presented graphically in respect of different considered field functions with load frequency and epicentral distance for 6 mm cadmium selenide (CdSe) material half-space.