In this article, we specially focused on rhombus silicate molecular structure. Graph is a data structure for describing complex systems, which contains a set of objects and relationships. A molecular graph, also known as a chemical graph, is a graph-theoretic representation of the structural formula of a chemical compound used in chemical graph theory and mathematical chemistry. A chemical graph is a labelled graph whose edges represent covalent bonds and vertices represent the atoms. A set of vertices (atoms) of a graph G is known as its dominating set with respect to the vertices, if every vertex other than that set is adjacent to some vertex in set. The vertex and edge dominating sets, to... More >

Three-dimensional (3D) flow of a viscoelastic fluid in the neighborhood of new family of modified stagnation point depending on shear to strain ratio over a flat surface is numerically investigated. Similarity equations are obtained from the fundamental conservation laws of mass, momentum, energy and nanoparticle concentration. The resulting set of nonlinear equations are solved numerically using an implicit finite difference scheme known as Keller-Box Method. A comparative analysis for modified Hiemenz flow, non-axisymmetric stagnation point and axisymmetric stagnation point flow is carried out. Velocity, temperature and concentration profiles, skin frictions local Nusselt and Sherwood numb... More >

In the current study, a new approach had been constructed to define new maps using the concept of bornological semi open and bornological semi closed sets, which includes sequential bornological semi continuous maps, bornological semi closed (open) maps, bornological strongly semi closed (open) maps, and bornological semi-irresolute closed (open) maps. We investigate and study the properties of these concepts. More >

This paper investigates the bio-convective behavior of a third-grade non-Newtonian nanofluid over a stretching sheet. While the influence of Newtonian fluid flow based on classical Fourier and Fick’s laws has been widely discussed in previous studies, this work focuses on a novel third-grade nanofluid model incorporating various physical effects. Notably, the classical Fourier law is replaced by the Cattaneo–Christov (CC) theory for both heat and mass fluxes, capturing relaxation phenomena in the presence of bioconvective effects. Heat and mass transport are modeled using the CC framework, and nanoscale mechanisms are described via the Buongiorno nanofluid model. The influences of thermo... More >

This study presents a mathematical framework to analyze the transmission dynamics of the Ebola Virus Disease (EVD) using an extended SEIRVH model. The model incorporates vaccinated and hospitalized compartments, addressing critical factors such as vaccination efficacy, healthcare interventions, and natural disease progression. Differential equations describe the transitions between six population compartments. The study evaluates model stability and bifurcation through well-posedness, positivity, and boundedness analyzes, ensuring realistic and biologically valid solutions. The basic reproduction number, R0, derived from the next generation matrix, serves as a threshold for outbreak control.... More >

This research contains the Hartmann boundary layer effectiveness in peristaltic flow of non-Newtonian viscoelastic fluids through asymmetric channel walls. Due to the Hartmann boundary layer, Hartmann number is considered very large. Porosity effects are included in view of modified Darcy's principle. Energy equation is modelled in the presence of viscous dissipation and Joule heating features. No slip condition for fluid velocity is considered at both channel walls. Large wavelength and dominating viscous forces implementation reduce the PDEs into ODEs. The resulting system of ODEs approximate solution is attained through perturbation and matching techniques for large magnetic field effects... More >

The simulations for non-Fourier heat transfer model has been performed for modified Eyring-Powell fluid, comprising the vairbale visocity. The interia outcomes for thermal problem are evaluated by interpreating the Darcy-Forchheimer features. The investigation for visualzing the heat transfer aspects is subject to variable thermal conductivty. The induction of flow is nonlinear moving surface. After developing the governing expressions, analytical treamtnet of problem is presented. The results are graphically presented to endorse physical aspects of current model. More >

This research focuses on the computational analysis and numerical investigation of BrCl ion density within an HBr-Cl_2 capacitively coupled plasma system. A two-dimensional fluid simulation model was developed to examine the influence of varying the HBr: Cl_2 gas ratio on BrCl ion formation. The simulation framework incorporates fundamental plasma fluid equations, including the continuity equation, momentum conservation equations, and energy conservation equations, along with appropriate boundary conditions. The investigation specifically explored gas composition variations ranging from 10% Cl_2 and 90% HBr to 90% Cl_2 and 10% HBr, incremented in 20% steps. The radio frequency (RF) driving f... More >

This study presents the application of the Artificial Neural Network Backpropagation Levenberg-Marquardt (ANN-BLMS) model for solving the nonlinear system of equations governing the flow of Casson-Williamson nanofluid under the influence of a magnetic field, Brownian motion, and thermophoresis effects. The model was trained using MATLAB's "bvp4c" solver to generate a reference dataset for various flow scenarios. Graphs having significant interest such as Nusselt Number are plotted and performance evaluation was carried out across multiple scenarios, which included variations in parameters such as Prandtl number, Weissenberg number, and Brownian motion coefficient. The results demonstrate tha... More >

The twenty-first century deals with two major problems that require speeding up technological progress alongside environmental preservation. The field of applied mathematics which used to function as a supporting tool now operates as a transformative engine which drives progress in thermal management, energy storage, nanofluidics, artificial intelligence and environmental modeling. The ICCK Journal of Applied Mathematics begins its first edition at the point where necessity and opportunity unite to enable cross-disciplinary research between theoretical models and technological implementation. More >