This article investigates the solvability and stability of a nonlinear tripled system of fractional integrodifferential equations via integral boundary conditions. We prove the fundamental existence and uniqueness results for the solution using powerful methods from nonlinear functional analysis, including the Banach fixed-point theorem. Crucially, we gauge the system's resistance to small perturbations using Ulam-Hyers stability analysis. Our results confirm that approximate solutions are close to the true solution, providing an essential resilience measure for complex models in which memory and hereditary traits are captured by fractional derivatives. Finally, an illustrative example has been presented to validate the stated theoretical results.
by of Commons permits In this article, we propose a new wavelet method for solving nonlinear Katugampola fractional differential equations on an arbitrary interval. We have introduced a new wavelet, which we named as the Katugampola Gegenbauer wavelet (KGW), and constructed its new operational matrices of Katugampola fractional integrations as well as Katugampola fractional derivatives. The Katugampola Gegenbauer wavelet and its operational matrices are combined with the Adomian polynomials to propose a new method for the solution of nonlinear Katugampola fractional differential equations. The purpose of using the Adomian polynomials is to handle the nonlinearities in the equations. Furthermore, we have provided a detailed methodology for implementing the proposed approach to nonlinear Katugampola fractional differential equations. A detailed error analysis is also performed for the proposed method. The proposed method is implemented on several nonlinear Katugampola fractional differential equations to show the reliability, efficiency, and accuracy of the method.
This study investigates the two-dimensional behavior of a nonlocal micropolar double-porous thermoelastic material with voids (MDPTMWV) within the framework of the Moore-Gibson-Thompson (MGT) theory. An isotropic, homogeneous, initially stressed, rotating thermoelastic half-space with double porosity is considered. The MGT heat conduction model, incorporating memory-dependent derivatives and variable thermal conductivity, is employed. Governing equations are derived using generalized thermoelasticity, and analytical solutions for displacement, temperature, equilibrated stress, and thermal stress components are obtained via Lame's potentials combined with normal mode analysis. The model is analyzed under boundary conditions including variable temperature, normal stress, constant equilibrated stress, and stress-free surfaces. Numerical evaluations using MATHEMATICA illustrate the effects of time, rotation, initial stress, and nonlocal parameters. The results indicate that double porosity and the considered parameters significantly amplify material responses, particularly under increasing time, rotation, initial stress, and nonlocal effects. Several special cases are discussed and validated against the literature. These findings provide insights relevant to geophysics, seismology, and earthquake engineering.
CC In this study, a new unit interval distribution defined on the unit interval is developed through a power transformation approach and termed the Power Unit Haq (PUH) distribution. Several key statistical properties of the new distribution are derived, including incomplete moments, moments, and associated measures, moment generating function, hazard function, mean residual life function, and R & eacute;nyi entropy. The parameters of the proposed distribution are estimated using five estimation approaches, and their performance is evaluated through extensive Monte Carlo simulations. The flexibility and practical relevance of the new distribution are further demonstrated by utilizing three real datasets-one involving radiation, reactor pump failures, and kidney dialysis patients. The proposed distribution exhibits superior fitting performance compared to established competing unit interval distributions. Additionally, Bayesian estimation of the model parameter is carried out, enhancing the distribution's applicability for real-world scenarios.
This paper proposes a new bounded probability model, the Unit-Weighted Lomax (UWLx) distribution, constructed via transformation of the weighted Lomax distribution. The UWLx distribution is designed for data restricted to the unit interval and provides greater flexibility in representing diverse behaviors of density and hazard functions, including monotonic and bathtub-shaped forms. Key statistical properties such as survival and hazard rate functions, moments, and order statistics are derived. Parameter estimation is addressed through the maximum likelihood method, and a simulation study confirms the consistency and efficiency of the estimators. The practical utility of the model is demonstrated through an application to COVID-19 recovery rate data, where the UWLx distribution is compared against well-known unit distributions, including the Beta, Kumaraswamy, and Unit Weibull. Model selection criteria and goodness-of-fit tests show that the UWLx distribution yields a superior fit, underscoring its potential as a versatile tool for analyzing bounded data in medical, reliability, and related fields. (c) 2026 The Author(s). Published by the OICC Press under the terms of the CC BY 4.0, Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
