2025-12-06
Aftab Ahmad, Mukhtar Ahmad, Yuhani Binti Yusof, Muhammad Muawwaz, Muhammad Maaz, Ather Qayyum
This research introduces a novel extension of the Caputo fractional derivative operator, characterized by a new parameter k >0. We establish several properties of the Caputo k-fractional derivative operator and present a series of results related to its application. Additionally, we extend the concept of k-hypergeometric functions and derive their integral representations utilizing the k-fractional derivative operator. Our work further includes the development of linear and bilinear generating relations for the extended k-hypergeometric functions, as well as the Mellin transform of selected extended k-fractional derivatives. Keywords: Caputo fractional derivative operator; k-fractional derivative operator; k-hypergeometric functions; linear generating relations; mellin transform; extended k-fractional derivatives. 2010 Mathematics Subject Classification. 26A30; 26A45; 26A48
2025-12-06
Akram Kohansal
In thispaper, the authors investigate the Bayesian inference of the m-component stress-strength parameter for the generalized inverse Weibull distribution under an adaptive hybrid progressive censoring scheme. The study considers three cases. In the first step, the paper employs the MCMC method to derive a Bayesian estimate of the m-component stress-strength parameter when both the common parameters for strengths and stress variables are unknown. Secondly, assuming that the common parameters are known, two approximation methods are employed: namely, the MCMC method and Lindley’s approximation. Finally, in a broader scenario where all parameters are distinct and undisclosed, the paper employs MCMC simulation to calculate a Bayesian estimate of the m-component stress-strength parameter. To evaluate and compare these methods’ performance, one Monte Carlo simulation is conducted. Additionally, a real data set is used to implement theoretical methods proposed in this study. Keywords: m-component stress-strength reliability; Lindley’s approximation; MCMC method; Adaptive hybrid progressive censoring scheme. 2010 Mathematics Subject Classification. 62N05; 62F15
2025-12-06
Ahmed Bouchenak, Iqbal M. Batiha, Mazin Aljazzazi, Iqbal H. Jebril, Fakhreddine Seddiki, Rasha Ibrahim Hajaj
Within this research, we introduce a new modified conformable operator and study its properties in detail. Furthermore, we investigate the self-adjoint modified conformable equation and its connection to modified conformable initial value problems. Additionally, we analyze the modified conformable Sturm–Liouville problem, determining its eigenvalues and corresponding eigenfunctions, while establishing results on orthogonality and dependence. Finally, illustrative examples are provided to demonstrate the applicability of our findings. Keywords: Modified conformable derivative; Modified conformable integral; Modified conformable Sturm Liouville problem; Modified conformable self adjoint equation; Orthogonality; Dependence. 2010 Mathematics Subject Classification. 34B24; 26A33
2025-12-06
Noorbhasha Rafi, M. Sambasiva Rao
In a pseudo-complemented Almost Distributive Lattice (pseudo-complemented ADL), the notions of coherent filters, strongly coherent filters, ♦-closed filters are introduced and their properties are studied. A set of equivalent conditions for any filter of a pseudo- complemented ADL to become a coherent filter is given. Also, the concept of median filters is introduced and a set of equivalent conditions for any maximal filter of a pseudo-complemented ADL to become a median filter is derived which leads to the characterization of a stone ADL. Keywords: strongly coherent filter; median filter;minimal prime filter; maximal filter; stone ADL. 2010 Mathematics Subject Classification. 06D99; 06D15
2025-12-06
Augustine Igwebuike Anya, Hajra Kaneez, Nnaemeka Stanley Aguegboh, Monalisa Chizoma Dike
The current research deals with the Mathematical solutions for the thermo-mechanical response of surface waves on a half-space with an inclined mechanical load on the corrugated-impedance surface influenced by magnetic field and thermal stress. We utilized the harmonic approach for wave analysis in determining the solution of the model. Using Green and Lindsay theory of thermoelasticity, the distribution fields of the system such as the thermal, normal and shear stresses, and the displacement components were analytically derived. Also, the behavior of the two times relaxation constants, special angles of various inclinations and the effect of magnetism, etc., on the distributions are graphically presented using MATHEMATICA 11 software. Our computational results show that an increase in the inclined angles (special and non-special angles) produces a corresponding increase in the distribution profiles of the surface wave. Also, increase in one of the thermal relaxation constants exhibited decreasing effects on the distribution profiles whilst the temperature profile increases in modulation. Thus, our result holds true for the thermal assumptions of the temperature distribution under the considered thermo-elasticity model. Also, researchers working in the area of non-destructive material testing and evaluation would find this investigation useful; owing to the grooved-impedance coloration of the material surface and the model in its entirety. Keywords: Relaxation times, impedance boundary, special angle of inclination, grooved boundary, magneto-thermal effects. 2010 Mathematics Subject Classification. 26A25; 26A35
2025-12-06
Abdulhameed Ado Osi, Usman Abubakar, Muftahu Zubairu Ringim
In this work, we introduce the Kumaraswamy Sine Inverted Rayleigh (KWSIR) distribution as an extension of the classical Inverse Rayleigh distribution, offering greater flexibility in modeling real-world data. The KWSIR distribution combines the Kumaraswamy and Sine Inverted Rayleigh distributions, resulting in a unimodal, right-skewed probability density function and an increasing or J-shaped hazard rate function. We explore key statistical properties, including the probability density function, cumulative distribution function, quantile function, moments, incomplete moments, entropy measures, and order statistics. Parameter estimation is conducted using the maximum likelihood method. To illustrate its applicability, we analyze a real-world dataset on bladder cancer, demonstrating the superior fitting performance of the KWSIR distribution. Keywords: Probability distribution; maximum likelihood estimation; moments, moment generating function. 2010 Mathematics Subject Classification. 26A25; 26A35
2025-12-06
C. A. Onate, M. O. Oluwayemi, K. O. Emeje
This study presents a comparative analysis of the eigenvalues, vibrational partition function, and vibrational enthalpy of the Hellmann potential under different quantum states, cyclotron frequencies, and temperatures. The study reveals that the eigenvalue at higher quantum states exhibit less negativity values, with the present method consistently yielding lower eigenvalues than the NU and AP methods. The effect of cyclotron frequency on eigenvalues indicates an upward energy shift with increasing frequency, while spacing between successive energy levels increases at higher quantum numbers. The vibrational partition function exhibits temperature-dependent behaviour, increasing steadily in some cases while showing fluctuations and saturation effects at specific values of cyclotron frequency. Similarly, the vibrational enthalpy trends suggest stabilization at higher temperatures, with variations in magnitude and rate of change depending on cyclotron frequency. These findings highlight the complex interplay between quantum state, cyclotron frequency, and thermal effects on the Hellmann potential system. Keywords: Bound state; Wave equation; Eigensolutions; Thermodynamic properties; Potential model. 2010 Mathematics Subject Classification. 26A25; 26A35
2025-12-06
Imen Badrani, Mondher Damak
In this paper, we extend the classical Itˆo formula by employing the framework of quantum calculus to derive its q-analogue, applicable to both classical Brownian motion and q-Itˆo processes via the quantum Taylor expansion. We also determine the q-infinitesimal generators associated with stochastic q-differential equations. To illustrate the applicability of our results, we present the q-Black-Scholes equation as a concrete example. Throughout the study, we assume 0 < q < 1, and we show that the classical results of Itˆo calculus are recovered in the limit as q → 1. Keywords: q-calculus; Itˆo calculus; semigroup; stochastic differential equations. 2010 Mathematics Subject Classification. 05A30; 60H05; 60H10; 60J65