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.
This study develops a detailed Lie symmetry analysis for the one-dimensional time-fractional Gross-Pitaevskii equation (TFGPE), emphasizing how the adopted fractional derivative-Riemann-Liouville (RL) versus Caputo-modifies the symmetry algebra, nonlocal conservation laws, and invariant solution families. The complex-valued model is rewritten as an equivalent coupled system of real partial differential equations, and the corresponding infinitesimal generators are derived in a unified and systematic manner for both fractional formulations. We show that, in the Caputo setting, the standard global U(1) phase invariance is retained, whereas in the RL formulation this key symmetry is destroyed because the associated initial data are not invariant and the fractional operator does not transform covariantly. Leveraging the resulting symmetry groups, we obtain similarity reductions and construct group-invariant solutions, and we further establish nonlocal conservation laws by applying Ibragimov's nonlinear self-adjointness approach. Overall, our findings indicate that the selection of the fractional derivative is not a purely technical choice; it decisively affects physical consistency, the admissible symmetry structure, and the conservation behavior of fractional quantum models. The analysis offers a direct RL-Caputo comparison and supports the Caputo derivative as the more suitable framework for preserving the inherent symmetries of quantum systems.
In this paper, we first establish the necessary conditions for the existence, uniqueness, and stability of solutions to system (1) by applying an alternative fixed-point theorem. We then provide specific examples and utilize the Banach fixed-point numerical method to demonstrate the applicability and reliability of our approach; notably, one of these examples is solved numerically in full, and the results from this numerical approximation further confirm the effectiveness and accuracy of the proposed method. These results verify the feasibility of the proposed approach for approximating solutions to complex fractional differential systems.
This paper investigates the numerical solution of a three-dimensional time -space fractional functional partial differential equation involving Caputo fractional derivatives in time and Riesz fractional derivatives in space. Owing to the inherent difficulties associated with fractional operators, such as weakly singular kernels and strong nonlocality, conventional numerical methods often encounter limitations in terms of accuracy and computational efficiency. To address these challenges, a hybrid numerical scheme is developed in which the Caputo fractional derivative is discretized by means of cubic spline interpolation, providing high-order temporal accuracy, while advanced meshless techniques are employed for the spatial approximation of the Riesz fractional derivative, thereby effectively managing its global support and singular behavior. The resulting fully discrete scheme is rigorously analyzed, and its unconditional stability is established using the energy method. Extensive numerical experiments on various three-dimensional domains demonstrate the high accuracy of the proposed method, with convergence rates consistent with the theoretical analysis, as well as favorable computational efficiency. Overall, the proposed approach offers a robust and flexible computational framework for the numerical treatment of complex fractional models arising in physics, engineering, and applied sciences.
This paper introduces a new and flexible family of continuous probability distributions, referred to as the Exponentiated Chen Marshall-Olkin family. The linear representation of the proposed model is derived, and several of its statistical properties, including moments, quantile function, R & eacute;nyi entropy, and reliability measures, are investigated. Parameter estimation for this family is discussed using the maximum likelihood method under both complete and right-censored samples, while three distance-based estimation approaches are also considered. A particular sub-model of this family, called the Exponentiated Chen Marshall-Olkin Weibull distribution, is also proposed and studied in detail. Its mathematical characteristics and related sub-models are explored, and four different estimation techniques-maximum likelihood, least squares, weighted least squares, and Anderson-Darling-are employed to estimate the unknown parameters. Furthermore, a comprehensive simulation study is conducted to assess the bias and mean square error of the estimators, followed by applications to real health and engineering datasets. The empirical results demonstrate that the Exponentiated Chen Marshall-Olkin family provides excellent flexibility for modeling data exhibiting skewness, heavy tails, reliability characteristics, and non-monotonic hazard rates, confirming its potential as a powerful tool in reliability and lifetime data analysis.
This study aims to develop an advanced model for the propagation of photo electro-magneto-thermoelastic waves in rotating, nonlocal semiconductor media subjected to pulsed laser beam. The novelty of this work lies in formulating a new coupled dynamic model that integrates photothermal, mechanical stresses and carrier density with temperature interactions in an elastic semiconductor medium. The resulting coupled system for temperature, displacement, stress, and plasma density is solved using the normal-mode technique under pulsed laser beam. Numerical simulations are carried out for Silicon material to explore the influence of the electro-magnetic field and rotation. Results show that lowering the rotation produces slower thermal decay and enhanced oscillations in displacement components, reflecting long-memory heat transport at the Nano scale. Electro-magnetic field significantly modifies temperature profiles and stress amplitudes, with stronger effects near the heated surface. Rotation affect wave dispersion, while the electro-magnetic field interaction governs energy absorption and stress localization. The research presents, for the first time, electro-magnetic field photo thermoacoustic formulation for rotating semiconductors with temperature-dependent conductivity. The model enriches the theoretical understanding of ultrafast laser-matter interactions, offering guidance for the design of semiconductor devices and MEMS sensors, diagnostics operating under rapid or high-intensity thermal loads. The results are represented graphically to assess the influences of the rotation and electromagnetic field on the plasma, thermal, and elastic waves.
This study contributes to the derivation of a bounded probability model for unit interval data analysis. The proposed model is named the Sine Unit Moment Exponential (SUME) distribution. This SUME model has the potential to model both the monotone increase and the bathtub shape for the hazard function. We investigate various statistical properties, including mixture representation, moments, quantile function, mean residual life function, and order statistics. The parameter estimation of the SUME distribution is discussed using six different estimation approaches. A comprehensive simulation study is performed to assess frequentist properties of the considered estimation methodologies. Two different datasets related to failure time and milk production are utilized to evaluate the practicality and flexibility of the proposed distribution over renowned unit interval distributions.
Transmuted distributions have gained attention in statistical modeling due to their flexibility and ability to enhance the performance of baseline distributions. In this article, we introduce the transmuted one-parameter Sarhan-Tadj-Hamilton distribution. Various structural properties of the proposed distribution, such as explicit expressions, stochastic orders, moments, and order statistics are derived. Six parameter estimation methods are examined, with their relative performance compared through Monte Carlo simulations and ranked across different sample sizes. The proposed model is further validated using multiple real data sets, demonstrating its practical flexibility.
This study investigates the impact of rotation on wave propagation within a micro-elongated thermo-elastic medium, employing the fractional conformable derivative under Lord-Shulman (L-S) theory, the Dual-Phase-Lag (DPL) model, and the Refined Dual-Phase-Lag (RDPL) model. The governing equations for heat conduction, mechanical motion, and micro-elongation are formulated to account for finite thermal wave speeds and microstructural effects. By applying non-dimensionalization and normal mode analysis, the coupled system is transformed into analytically solvable form. Explicit solutions for displacement, temperature, stress, and micro-elongation fields are obtained. Numerical results compare L-S, DPL, and RDPL models with and without rotation, and assess the effect of fractional order. The results show that rotation significantly influences wave propagation characteristics such as amplitude, speed, and attenuation.
In this study, we introduce a novel and highly flexible probability model, called the Novel Exponentiated G-family distribution (NEGFD), which serves as a general framework for generating new probability models. We apply this framework to the Frechet distribution, resulting in the Novel Exponentiated G-family Frechet distribution (NEGFFD), which extends the classical Frechet model by incorporating greater flexibility in modeling skewness and tail behavior. Rooted in the broader class of exponentiated G-families, this approach enhances modeling flexibility, making it particularly effective for capturing skewed and heavy-tailed patterns commonly observed in empirical data. Theoretical aspects of the model are rigorously developed, including derivations of its moments, incomplete moments and hazard rate function. To evaluate the performance of parameter estimation, a detailed Monte Carlo simulation study is conducted using the method of maximum likelihood estimation (MLE) under various sample sizes. The simulation findings demonstrate the consistency, efficiency, and robustness of the maximum likelihood estimates (MLEs) across different scenarios. The practical usefulness of the proposed distribution is illustrated through its application to real-world dataset; epidemiological data and environmental data. In both domains, the model exhibits superior performance compared to the classical Frechet and related competing models, as evidenced by lower values of standard model selection criteria. Additional graphical diagnostics and non-parametric goodness-of-fit assessments further support the proposed model's effectiveness and flexibility in real data modeling contexts.
This paper introduces a new smoothed bootstrap technique for analyzing double-censored data. The method is implemented based on a variant of Hill's A(n) assumption adapted for the double-censored setting. Through simulation studies, we compare the proposed approach with Efron's classical bootstrap, focusing on the coverage accuracy of quartiles in bootstrap confidence intervals. The results indicate that the new smoothed bootstrap generally outperforms Efron's method, particularly for small to medium-sized datasets.
A new two-parameter mixed Poisson distribution is introduced and explored in this study. The new model is named the Poisson Ramos Louzada Exponential distribution. Various statistical characteristics of the new count distribution are derived and studied, including moments, generating function, overdispersion, failure rate, reversed hazard function, cumulative hazard function, Mills ratio, odd function, and order statistics. A novel regression model is also introduced based on this distribution. The parameters of the new probability model are estimated using the maximum likelihood estimation approach. The estimation behaviour of these derived estimators is studied using a Monte Carlo simulation study. The flexibility and adaptability of the new distribution have been confirmed using two datasets related to radiation and corn borer. The results reveal that the proposed distribution is efficient and competitive with existing count models.
This paper introduces a novel family of cos-robust regression-type estimators along with special members to estimate the finite population mean under SRSWOR. The new family of estimators is produced by hybridizing the auxiliary information with the cos function. To reduce the impact of outliers, various robust regression techniques, namely Huber's M-estimation, Mallows' GM-estimation, Schweppe's GM-estimation, and SIS GM-estimation, are employed and theoretically compared with the Ordinary Least Squares (OLS) method. Simulated and actual data are used to generate and validate theoretical properties, such as bias and Mean Square Error (MSE). According to the findings, the robust estimators perform better than the conventional OLS approach in terms of MSE and PRE.
We propose the Iterated Flexible Arnoldi-Tikhonov (IFAT) method for large-scale discrete ill-posed problems. IFAT embeds nonstationary Tikhonov updates into a flexible Arnoldi reduction whose basis is enriched with problem-aware directions, enabling regularization in subspaces that standard Arnoldi and classical projected Tikhonov schemes may fail to capture. Building on the Arnoldi-based preconditioner of Buccini-Onisk-Reichel and recent projected/iterated frameworks with adaptive parameter choice, we (i) unify flexible subspace enrichment with discrepancy-principle parameter selection on the reduced problem, (ii) derive a residual update that requires no additional matrix-vector products, and (iii) establish monotone error decrease and stability under inherited spectral-equivalence assumptions. Extensive experiments in image deblurring, signal reconstruction, tomography, MRI, seismic deconvolution, and electrical impedance tomography demonstrate that IFAT achieves consistently higher reconstruction quality (PSNR/SSIM, SNR/CNR, EPI) with approximately 40-60% fewer outer iterations than IAT and classical Tikhonov. Additional comparisons with Landweber and damped Gauss-Newton show that IFAT converges substantially faster than gradient-based schemes and is less sensitive to noise amplification than second-order approaches. Against the best published baselines from BOR (2023) and PIT-GF (2025), IFAT attains lower or comparable relative reconstruction error at the same discrepancy breakout. These results indicate that flexible augmentation provides a robust and practically significant improvement over fixed-subspace methods for real-world inverse problems.
A recent study proposed a groundbreaking pathwise approximation method for numerically solving stochastic differential equations (SDEs) driven by Brownian motions. This approach eliminates the necessity of simulating stochastic It & ocirc; integrals, denoted by 3a. Instead, these integrals are replaced with random variables that maintain the same moments under the linear term condition. The main objective of this method is to deliver approximate solutions with an error rate of O(h 3 2 ). This level of precision significantly exceeds the strong V error rates achieved by the Euler and Milstein methods, which are O( h) and O(h), respectively, where h represents the step size. The development of this method relies on the assumption that the diffusion process is nondegenerate and incorporates the It & ocirc;-Taylor expansion alongside a modified perturbation approach. In this paper, we demonstrate that the scheme achieves strong convergence in the Wasserstein distance with an order of O (h 3 2 ) by leveraging techniques from the optimal transport theory.
This study aims to acquire numerical schemes to detect the numerical solutions of fractional partial differential equations of arbitrary order, subject to prescribed initial and boundary conditions. This novel approach, referred to as the Green-CAS technique, integrates Green's function with CAS wavelets to construct an efficient and systematic computational framework. The present approach is not only simple and easy to implement due to the Green function, but it also eliminates the need for operational matrices for boundary conditions. To further enhance computational efficiency, a fast algorithm is coupled with the Green-CAS wavelets, enabling effective handling of fractional partial differential equations. While tackling the nonlinear fractional partial differential equation of arbitrary order, the Picard iterative method is employed to transform the equation into a sequence of linear problems, which are then solved using the proposed techniques. Moreover, the order of convergence for two parameters has also been demonstrated in the convergence analysis, which further strengthens the effectiveness of the proposed technique. To show the validity and accuracy of the recommended techniques, the acquired outcomes are compared with the conventional CAS wavelets and various other renowned techniques. In addition, the results of various applications are presented in the form of graphics and tables, which elaborate on the effectiveness and correctness of the discussed method.
