International Journal of Advancements in Mathematics <p>International Journal of Advancements in Mathematics is an international, open access journal that provides an advanced forum for mathematical science research. International Journal of Advancements in Mathematics is a scholarly publication that aims to disseminate high-quality research in the field of mathematics. <em> </em>The journal publishes rigorously peer-reviewed articles that cover a broad range of topics, including pure mathematics and applied mathematics. Additionally, the journal welcomes articles that demonstrate the diverse applications of mathematics in various fields of science, such as engineering, physics, and computer science. </p> en-US (Editor-in-Chief: Dr. Azmat Ullah Khan Niazi ) (Muhammad Naeem) Sat, 09 Sep 2023 00:00:00 +0000 OJS 60 Existence, uniqueness and stability analysis of fractional-order neural networks with multiple delays and variable coefficients: Banach fixed point approach <p>This study uses the Banach fixed point idea and analysis technique to explore the existence, uniqueness, and stability of solutions for a class of fractional-order neural networks. For fractional-order neural networks with multiple time delays and variable coefficients, a necessary situation is stated to guarantee the uniqueness, existence, and uniform solutions of stability. The outcomes are simple to confirm in practice and, to a certain extent, build upon and extend several prior initiatives. An excellent example is given to illustrate how the findings might be applied and relied upon.</p> Kanwal Niazi, Naveed Ahmed, Aneela Umar, Kiran Pasha Copyright (c) 2023 Kanwal Niazi, Naveed Ahmed, Aneela Umar, Kiran Pasha Sat, 28 Oct 2023 00:00:00 +0000 Convection in a triangular enclosure with a left wall heated either uniformly or non-uniformly, using a water-CuNanofluid and in the presence of a magnetic field <p>An incompressible steady nanofluid flow through an isosceles triangular the tube in the presence of a magnetic field is the subject of a numerical investigation for heat transfer in this publication. Pressure is removed from the governing equations using the penalty approach. Equations that were produced and solved using the Galerkin weighted residual method. For this flow issue, we assumed that the cavity's left wall would be heated uniformly or unevenly while the cavity's right and bottom walls would remain cool.</p> <p>Results are calculated for a variety of factors, such as the Hartman number <em>Ha</em> (), Rayleigh number <em>Ra</em> (), and Heat generation/absorption coefficient <em>q </em>() while, Prandtle number &nbsp;and Solid volume fraction &nbsp;&nbsp;are held constant at 6.2 and 0.03, respectively.</p> <p>Figures are used to present these computed results in terms of Nusselt numbers, stream functions and isotherms. It has been observed that, for uniform heating, the strength of stream line circulations increases with an increase in the Rayleigh number , while the strength of stream line circulations decreases with an increase in the Hartman number. Where increasing heat absorption coefficient <em>q</em>, increases circulation strength and circulation cell moves to left wall in presence of heat sink and moves to cold right wall in presence of heat source .</p> <p>When a heat source &nbsp;is present in the cavity and a non-uniformly heated left wall is present, a higher temperature gradient is seen in the cavity. Isotherms are clustered to the left wall in the lower portion of the cavity and to the right wall in the upper portion, while isotherms near the bottom wall appear to be straight and parallel to the -axis.</p> <p>However, the nusselt number along the bottom wall Nu-B rises with the increasing values of x, while Nu-L along the left wall first increases and then decreases, and Nu-R along the right wall decreases first and then increases with distance. On the other hand, the heat transfer rate is observed to be higher for smaller values of &nbsp;along all the walls of the cavity.</p> Muhammad Umair, Aamir Mehmood, Muhammad Noman, Aqsa Aslam Copyright (c) 2023 Muhammad Umair, Umair Malik Thu, 28 Dec 2023 00:00:00 +0000 Shape effects of gold nanoparticles on squeezing nanofluid flow and heat transfer between parallel plates <p>The current paper examines how the form of gold (Au) nanostructures affects the compression of nanofluids and heat transmission across parallel surfaces. Water has been used as the porous medium to explore the various morphologies of nanomaterials, including columns, spheres, hexahedron, tetrahedron, and lamina. In order to create (ODEs), proper modifications must be applied to (PDEs). To solve nonlinear boundaries value regular differential equations statistically, the homotopy analysis method (HAM) guarantees converging of the numerical integration. On temperature and velocity profiles the impacts of several variables, including a solid volume fraction, thermal radiation, Reynolds number, magnetic field, Eckert number, sucking component, and slope angle, are represented graphically. The Nusselt is studied graphically for different values of the relevant factors. The obtained data show that, in comparison to other shapes of nanoparticles, lamina-shaped nanoparticles have the highest rate of heat transport and that sphere-shaped nanoparticles have played a significant role in thermal dispersion.</p> Aneela Umar, Naveed Ahmed Copyright (c) 2023 Aneela Umar Sun, 25 Jun 2023 00:00:00 +0000