https://ijmaa.in/index.php/ijmaa <p><strong>International Journal of Mathematics And its Applications (IJMAA)</strong> is an international single-blind confidential peer-reviewed online academic research journal in all the streams of mathematics and its applications. The journal's vision is to create a forum for review, reflection, and discussion informed by the results of recent and ongoing research in every field of mathematics. IJMAA encourages new ideas and works in mathematics and its applications, and it publishes high-quality original papers, theory-based empirical papers, review papers, and case reports. IJMAA will also occasionally publish, as special issues, proceedings of international conferences or dedicated to various important scientific events and/or anniversaries.</p> JS Publication en-US International Journal of Mathematics And its Applications 2347-1557 https://ijmaa.in/index.php/ijmaa/article/view/1465 <p>In this study, we explore a universe characterized by Anisotropic and Homogeneous Bianchi Type-V geometry, filled with both Dark Matter (DM) and Dark Energy (DE) within the framework of General Theory of Relativity. We introduce an interaction between DM and DE, incorporating Tsallis generalized entropy. The field equations are solved using the constant deceleration parameter proposed by Berman (1983). The Equation of State (EoS) parameter of Tsallis Holographic Dark Energy (THDE) elucidates the current accelerated expansion of the universe, exhibiting Phantom-like and approaching $\Lambda {CDM}$. Additionally, we calculate the EoS parameter, Anisotropy Parameter, Deceleration Parameter, and Total Energy Density parameter. Our results align well with observational data.</p> Vaibhav D. Bokey Copyright (c) 2024 International Journal of Mathematics And its Applications https://creativecommons.org/licenses/by-nc/4.0 2024-04-30 2024-04-30 12 2 1 10 https://ijmaa.in/index.php/ijmaa/article/view/1467 <p>The Laplace transform, Elzaki transform, and Sumudu transform methods are used in this paper to solve initial value problems directly without having to convert them to ordinary differential equations. One of the three methods can be used to solve initial value problems using these transformation techniques. By applying the relevant transform to the governing equation and initial conditions, initial value problems can be addressed using the Laplace, Elzaki, and Sumudu transform methods. By doing this, problems can be solved without having to convert them to ODE form. Transforming the initial value problems directly leads to solutions being obtained in one of the three proposed approaches: Laplace, Elzaki, or Sumudu. The added complexity of transforming problems to ODEs before using transforms to find solutions is avoided by this reformulation.</p> F. A. Almostafa Hekmat. M. Elnile Manel Belkhamsa Randa Eltayeb Sana Hafdhi Copyright (c) 2024 International Journal of Mathematics And its Applications https://creativecommons.org/licenses/by-nc/4.0 2024-04-30 2024-04-30 12 2 11 18