https://www.earthlinepublishers.com/index.php/ejms <p style="text-align: justify;">The Earthline Journal of Mathematical Sciences (E-ISSN: 2581-8147) is a peer-reviewed international journal dedicated to the publication of original research articles, review papers, and short communications that advance knowledge in pure and applied mathematics and their interdisciplinary applications.</p> Earthline Publishers, Madanambedu, Chittoor, Andhra Pradesh, India en-US Earthline Journal of Mathematical Sciences 2581-8147 <p><img src="https://earthlinepublishers.com/public/site/images/ejcs/88x311.png"><br>This work is licensed under a&nbsp;<a href="http://creativecommons.org/licenses/by/4.0/" rel="license">Creative Commons Attribution 4.0 International License</a>.</p> https://www.earthlinepublishers.com/index.php/ejms/article/view/1197 <p>This paper presents a rigorous comparative review of five pivotal integral transforms: Laplace, Sumudu, Elzaki, Aboodh, and the recently introduced RAHMOH transform. We establish a unified theoretical framework to analyze kernel structures, derive the complex inversion formula for the RAHMOH operator, and formally prove its mathematical equivalence to the Laplace transform. Unlike previous surveys, we derive analytical solutions for integer-order ODEs and PDEs, as well as fractional differential equations (FDEs) using all methods, confirming that while they are mathematically isomorphic, they differ significantly in algebraic pathways. Specifically, the analysis identifies the RAHMOH transform as a generalized ''bridge'' operator, encapsulating the scaling properties of Sumudu and the decay properties of Laplace through its dual-variable kernel. Furthermore, numerical simulations via MATLAB validate the consistency of the RAHMOH transform, demonstrating its dimensional stability and accuracy in modeling both dissipative and fractional systems.</p> Mohamed Hamad Musa Adam Oladele Yusuf Olatunji Rahma Farah Copyright (c) 2026-03-25 2026-03-25 16 3 373 391 10.34198/ejms.16326.27.373391 https://www.earthlinepublishers.com/index.php/ejms/article/view/1199 <p>This article focuses on creating new integral inequalities based on, and derived from, the classical Hermite-Hadamard integral inequality for convex functions. A key aspect of these developments is the use of integration by parts. One of the results obtained provides an alternative perspective under a specific smoothness assumption.</p> Christophe Chesneau Copyright (c) 2026-03-28 2026-03-28 16 3 393 399 10.34198/ejms.16326.28.393399