Earthline Journal of Mathematical Sciences

A Rigorous Review of Recent Integral Transforms for Solving Differential Equations: Analysis, Properties and Applications

2026-03-25T16:24:00+00:00

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.

Hadamard-Hermite Integral Inequality: An Integration by Parts Point of View

2026-03-28T15:08:56+00:00

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.

Computing Radial Anomaly in Kepler’s Equation via Weierstrass Elliptic Function

2026-04-13T16:45:22+00:00

The Weierstrass elliptic function is presented in the light of the astrodynamical equation. We synchronise the Weierstrass elliptic function with the elliptic curve which relates the set of Sato weights with the genus $(n,s)$, where $n<s$ and $n$, $s$ are co-prime, making all equations homogeneous. The duplication formula of the Weierstrass formula, as previously used in Uwamusi [14], is introduced as an indicator of how the function behaves near and far away from the origin of a complex number. The differential equation satisfied by the Weierstrass function is explained, and the invariant discriminant function of the Weierstrass elliptic function is taken as an important tool. A method for speeding up the computation process in the radial anomaly in Kepler’s equation, which provides the time of root passage between a pseudo-time and a stable variable time, is introduced via the Chebyshev–Halley iteration formula of third order in the light of the Weierstrass elliptic function. This thus provides in-depth information regarding the radius of peri-center passage and the real root closest to the exact solution. Also in the paper is a computation of the Schwarzian derivative for the Weierstrass elliptic function. Numerical examples are demonstrated with these methods, and the results obtained are quite impressive.

Mathematical Model of a Four Wheel Conventional Robot

2026-04-14T16:43:49+00:00

Mobile robot creation, control, and optimization demand adaptive and efficient strategies. The motion of a four-wheel mobile robot is considered. The four wheels are organized in pairs, with each pair set up as a differential drive system. The robot’s motion is analyzed at both kinematic and dynamic levels. Simulation tests validate the proposed algorithm, and the impact of the forces on the wheels is discussed, leading to key conclusions.

Generalized Rational Suzuki-Type Contractions in Double Controlled Metric Spaces with Applications

2026-04-14T17:08:47+00:00

In this paper, we introduce a new class of generalized rational Suzuki-type contractions in the setting of double controlled metric spaces. This framework extends controlled metric spaces by incorporating two independent control functions, thereby providing a more flexible structure for the analysis of nonlinear mappings. We establish an existence and uniqueness theorem for fixed points under this new contractive condition, which unifies and generalizes several known results in metric, $b$-metric, and controlled metric spaces. In addition, we investigate fundamental properties of the proposed framework, including a characterization via Picard iteration, Ulam--Hyers stability, convergence rate estimates, and data dependence of fixed points. As an application, we study the existence and uniqueness of solutions to a nonlinear Fredholm integral equation, showing that the proposed approach accommodates nonlinear kernels under weaker conditions than classical methods. The results contribute to the development of fixed point theory in generalized metric structures and provide a robust analytical tool for nonlinear problems arising in applied mathematics.