Search Results (4,098)

This work introduces a new family of multivariate hybrid special polynomials, motivated by their growing relevance in mathematical modeling, physics, and engineering. We explore their core properties, including recurrence relations and shift operators, within a unified structural framework. By employing the factorization method, we derive various governing equations such as differential, partial differential, and integrodifferential equations. Additionally, we establish a related fractional Volterra integral equation, which broadens the theoretical foundation and potential applications of these polynomials. To support the theoretical development, we carry out computational simulations to approximate their roots and visualize the distribution of their zeros, offering practical insights into their analytical behavior. Full article

This paper focuses on the problem, claimed in some works, of the non-existence of finite-time stable equilibria in nonlinear fractional differential equations. After dividing the equilibrium point into the initial equilibrium point and the finite-time equilibrium point, we provide sufficient conditions for the equilibrium point of a fractional stochastic differential equation. Then the finite-time stability of the equilibrium points of nonlinear fractional stochastic differential equations is presented. Finally, the correctness of the theoretical analysis is illustrated through an example. Full article

The successful transmission of Trypanosoma cruzi, the causative agent of Chagas disease, depends on intricate interactions with its insect vector. In Mexico, Meccus pallidipennis is a relevant triatomine species involved in the parasite’s life cycle. In the gut of these insects, the parasite moves from the anterior midgut (AMG) to the posterior midgut (PMG), where it multiplies. Finally, T. cruzi differentiates into its infective form by metacyclogenesis in the proctodeum or rectum (RE). This study aimed to characterize and compare the protein and glycoprotein profiles of the anterior midgut (AMG) and rectum (RE) of M. pallidipennis, and to assess their potential association with T. cruzi metacyclogenesis, with special attention to sex-specific differences. Insects were infected with the T. cruzi isolate ITRI/MX/12/MOR (Morelos). Protein profiles were analyzed by polyacrylamide gel electrophoresis, while glycoproteins were detected using ConA, WGA, and PNA lectins. The metacyclogenesis index was calculated for male and female triatomines. A lower overlap of protein fractions was found in the RE compared to the AMG between sexes, suggesting functional sexual dimorphism. Infected females showed greater diversity in glycoprotein patterns in the RE, potentially related to higher blood intake and parasite burden. The metacyclogenesis index was significantly higher in females than in males. These findings highlight sex-dependent differences in gut protein and glycoprotein profiles in M. pallidipennis, which may influence the efficiency of T. cruzi development within the vector. Further proteomic studies are needed to identify the molecular components involved and clarify their roles in parasite differentiation and suggest new targets for disrupting parasite transmission within the vector. Full article

Cardiovascular disease (CVD) and dementia may share common pathogenic factors such as atherosclerosis and hyperlipoproteinemia. Dyslipidemia-induced oxidative stress contributes to dementia comorbidity in CVD. Abelmoschus esculentus (AE, okra) potentiates in alleviating hyperlipidemia and diabetes-related cognitive impairment. This study evaluated the effects of AE in hyperlipidemic ApoE^−/− mice treated with streptozotocin (50 mg/kg) and fed a high-fat diet (17% lard oil, 1.2% cholesterol). AE fractions F1 or F2 (0.65 mg/kg) were administered for 8 weeks. AE significantly reduced serum LDL-C, HDL-C, triglycerides, and glucose, improved cognitive and memory function, and protected hippocampal neurons. AE also lowered oxidative stress markers (8-hydroxy-2′-deoxyguanosine, 8-OHdG) and modulated neuronal nuclei (NeuN) and doublecortin (DCX) expression. In vitro, AE promoted neurite outgrowth and neuronal differentiation in retinoic acid (RA)-differentiated human SH-SY5Y cells under metabolic stress (glucose and palmitate), alongside the upregulation of heme oxygenase-1 (HO-1), Nuclear factor-erythroid 2-related factor 2 (Nrf2), and brain-derived neurotrophic factor (BDNF). These findings suggest AE may counter cognitive decline via oxidative stress regulation and the enhancement of neuronal differentiation. Full article

Asymmetric functional-order (variable-order) fractional diffusion–wave equations (FO-FDWEs) introduce considerable computational challenges, as the fractional order of the derivatives can vary spatially or temporally. To overcome these challenges, a novel spectral method employing generalized fractional-order Chelyshkov wavelets (FO-CWs) is developed to efficiently solve such equations. In this approach, the Riemann–Liouville fractional integral operator of variable order is evaluated in closed form via a regularized incomplete Beta function, enabling the transformation of the governing equation into a system of algebraic equations. This wavelet-based spectral scheme attains extremely high accuracy, yielding significantly lower errors than existing numerical techniques. In particular, numerical results show that the proposed method achieves notably improved accuracy compared to existing methods under the same number of basis functions. Its strong convergence properties allow high precision to be achieved with relatively few wavelet basis functions, leading to efficient computations. The method’s accuracy and efficiency are demonstrated on several practical diffusion–wave examples, indicating its suitability for real-world applications. Furthermore, it readily applies to a wide class of fractional partial differential equations (FPDEs) with spatially or temporally varying order, demonstrating versatility for diverse applications. Full article

This paper proposes a novel analytical method to address the Helmholtz fractional differential equation by combining the Aboodh transform with the Adomian Decomposition Method, resulting in the Aboodh–Adomian Decomposition Method (A-ADM). Fractional differential equations offer a comprehensive framework for describing intricate physical processes, including memory effects and anomalous diffusion. This work employs the Caputo–Fabrizio fractional derivative, defined by a non-singular exponential kernel, to more precisely capture these non-local effects. The classical Helmholtz equation, pivotal in acoustics, electromagnetics, and quantum physics, is extended to the fractional domain. Following the exposition of fundamental concepts and characteristics of fractional calculus and the Aboodh transform, the suggested A-ADM is employed to derive the analytical solution of the fractional Helmholtz equation. The method’s validity and efficiency are evidenced by comparisons of analytical and approximation solutions. The findings validate that A-ADM is a proficient and methodical approach for addressing fractional differential equations that incorporate Caputo–Fabrizio derivatives. Full article

Background: Type 2 diabetes (T2D) is a global health epidemic with rising prevalence within Asian populations, particularly amongst individuals with high visceral adiposity and ectopic organ fat, the so-called Thin-Outside, Fat-Inside phenotype. Metabolomic and microbiome shifts may herald T2D onset, presenting potential biomarkers and mechanistic insight into metabolic dysregulation. However, multi-omics datasets across ethnicities remain limited. Methods: We performed cross-sectional multi-omics analyses on 171 adults (99 Asian Chinese, 72 European Caucasian) from the New Zealand-based TOFI_Asia cohort at 4-years follow-up. Paired plasma and faecal samples were analysed using untargeted metabolomic profiling (polar/lipid fractions) and shotgun metagenomic sequencing, respectively. Sparse multi-block partial least squares regression and discriminant analysis (DIABLO) unveiled signatures associated with ethnicity, glycaemic status, and sex. Results: Ethnicity-based DIABLO modelling achieved a balanced error rate of 0.22, correctly classifying 76.54% of test samples. Polar metabolites had the highest discriminatory power (AUC = 0.96), with trigonelline enriched in European Caucasians and carnitine in Asian Chinese. Lipid profiles highlighted ethnicity-specific signatures: Asian Chinese showed enrichment of polyunsaturated triglycerides (TG.16:0_18:2_22:6, TG.18:1_18:2_22:6) and ether-linked phospholipids, while European Caucasians exhibited higher levels of saturated species (TG.16:0_16:0_14:1, TG.15:0_15:0_17:1). The bacteria Bifidobacterium pseudocatenulatum, Erysipelatoclostridium ramosum, and Enterocloster bolteae characterised Asian Chinese participants, while Oscillibacter sp. and Clostridium innocuum characterised European Caucasians. Cross-omic correlations highlighted negative correlations of Phocaeicola vulgatus with amino acids (r = −0.84 to −0.76), while E. ramosum and C. innocuum positively correlated with long-chain triglycerides (r = 0.55–0.62). Conclusions: Ethnicity drove robust multi-omic differentiation, revealing distinctive metabolic and microbial profiles potentially underlying the differential T2D risk between Asian Chinese and European Caucasians. Full article

This study investigates a modified five-dimensional chaotic system by incorporating structural term adjustments and Caputo fractional-order differential operators. The modified system exhibits significantly enriched dynamic behaviors, including offset boosting, phase trajectory rotation, phase trajectory reversal, and contraction phenomena. Additionally, the system exhibits bidirectional transitions—conservative-to-dissipative transitions governed by initial conditions and dissipative-to-conservative transitions controlled by fractional order variations—along with a unique chaotic-to-quasiperiodic transition observed exclusively at low fractional orders. To validate the system’s physical realizability, a signal processing platform based on Digital Signal Processing (DSP) is implemented. Experimental measurements closely align with numerical simulations, confirming the system’s feasibility for practical applications. Full article

In this study, we focus on solving the nonlinear time-fractional Hirota–Satsuma coupled Korteweg–de Vries (KdV) and modified Korteweg–de Vries (MKdV) equations, using the Yang transform iterative method (YTIM). This method combines the Yang transform with a new iterative scheme to construct reliable and efficient solutions. Readers can understand the procedures clearly, since the implementation of Yang transform directly transforms fractional derivative sections into algebraic terms in the given problems. The new iterative scheme is applied to generate series solutions for the provided problems. The fractional derivatives are considered in the Caputo sense. To validate the proposed approach, two numerical examples are analysed and compared with exact solutions, as well as with the results obtained from the fractional reduced differential transform method (FRDTM) and the q-homotopy analysis transform method (q-HATM). The comparisons, presented through both tables and graphical illustrations, confirm the enhanced accuracy and reliability of the proposed method. Moreover, the effect of varying the fractional order is explored, demonstrating convergence of the solution as the order approaches an integer value. Importantly, the time-fractional Hirota–Satsuma coupled KdV and modified Korteweg–de Vries (MKdV) equations investigated in this work are not only of theoretical and computational interest but also possess significant implications for achieving global sustainability goals. Specifically, these equations contribute to the Sustainable Development Goal (SDG) “Life Below Water” by offering advanced modelling capabilities for understanding wave propagation and ocean dynamics, thus supporting marine ecosystem research and management. It is also relevant to SDG “Climate Action” as it aids in the simulation of environmental phenomena crucial to climate change analysis and mitigation. Additionally, the development and application of innovative mathematical modelling techniques align with “Industry, Innovation, and Infrastructure” promoting advanced computational tools for use in ocean engineering, environmental monitoring, and other infrastructure-related domains. Therefore, the proposed method not only advances mathematical and numerical analysis but also fosters interdisciplinary contributions toward sustainable development. Full article

The southern Great Xing’an Range is located in the overlap zone of the Paleo-Asian Ocean metallogenic domain and the Circum-Pacific metallogenic domain. It hosts numerous Sn-polymetallic deposits, such as Weilasituo, Bianjiadayuan, Huanggang, and Dajing, and witnessed multiple episodes of magmatism during the Late Mesozoic. The study area is situated within the Huanggangliang-Ganzhuermiao metallogenic belt in the southern Great Xing’an Range. The region has witnessed extensive magmatism, with Mesozoic magmatic activities being particularly closely linked to regional mineralization. We present petrographic, zircon U-Pb chronological, lithogeochemical, and Lu-Hf isotopic analyses of the Yexilinhundi granites. The results indicate that the granite porphyry and granodiorite were emplaced during the Late Jurassic. Both rocks exhibit high SiO₂, K₂O + Na₂O, differentiation index (DI), and 10,000 Ga/Al ratios, coupled with low MgO contents. They show distinct fractionation between light and heavy rare earth elements (LREEs and HREEs), exhibit Eu anomalies, and have low whole-rock zircon saturation temperatures (T_zr), collectively demonstrating characteristics of highly fractionated I-type granites. The εHf(t) values of the granites range from 0.600 to 9.14, with young two-stage model ages (T_DM2 = 616.0~1158 Ma), indicating that the magmatic source originated from partial melting of Mesoproterozoic-Neoproterozoic juvenile crust. This study proposes that the granites formed in a post-collisional/post-orogenic extensional setting associated with the subduction of the Mongol-Okhotsk Ocean, providing a scientific basis for understanding the relationship between the formation of Sn-polymetallic deposits and granitic magmatic evolution in the study area. Full article

In this work, we study Caputo fractional boundary value problems and contribute to the theory of fractional differential equations by improving the results of Ferreira. Specifically, we establish sharper bounds for the Green’s functions associated with the problems and apply Rus’s fixed-point theorem. Our results hold under a less restrictive assumption, thereby extending the class of problems for which the existence and uniqueness of solutions can be ensured. This is demonstrated through numerical validation presented in the final stage of our analysis. An important aspect of this approach is that it avoids the need for strong contraction conditions, suggesting potential applicability to a broader range of differential equations. Full article

Background and Objectives: Heart failure (HF) and chronic kidney disease (CKD) frequently coexist and are closely interrelated, significantly affecting clinical outcomes. Among CKD-related markers, albuminuria and estimated glomerular filtration rate (eGFR) have emerged as key prognostic indicators in HF. However, their specific predictive value across different HF phenotypes—namely HF with preserved ejection fraction (HFpEF) and HF with reduced ejection fraction (HFrEF)—remains incompletely understood. This systematic review aims to evaluate the prognostic significance of albuminuria and eGFR in patients with HF and to compare their predictive roles in HFpEF versus HFrEF populations. Materials and Methods: We conducted a systematic search of major databases to identify clinical studies evaluating the association between albuminuria, eGFR, and adverse outcomes in HF patients. Inclusion criteria encompassed studies reporting on cardiovascular events, all-cause mortality, or HF-related hospitalizations, with subgroup analyses based on ejection fraction. Data extraction and quality assessment were performed independently by two reviewers. Results: Twenty-one studies met the inclusion criteria, including diverse HF populations and various biomarker assessment methods. Both albuminuria and reduced eGFR were consistently associated with increased risk of mortality and hospitalization. In HFrEF populations, reduced eGFR demonstrated stronger prognostic associations, whereas albuminuria was predictive across both HF phenotypes. Heterogeneity in study design and outcome definitions limited comparability. Conclusions: Albuminuria and eGFR are valuable prognostic biomarkers in HF and may enhance risk stratification and clinical decision-making, particularly when integrated into clinical assessment models. Differential prognostic implications in HFpEF versus HFrEF highlight the need for phenotype-specific approaches. Further research is warranted to validate these findings and clarify their role in guiding personalized therapeutic strategies in HF populations. Limitations: The current evidence base consists primarily of observational studies with variable methodological quality and inconsistent reporting of effect estimates. Full article

The primary objective of this work is to develop a comprehensive theory of weighted fractional Sobolev spaces within the framework of timescales. To this end, we first introduce a novel class of weighted fractional operators and rigorously define associated weighted integrable spaces on timescales, generalising classical notions to this non-uniform temporal domain. Building upon these foundations, we systematically investigate the fundamental functional-analytic properties of the resulting Sobolev spaces. Specifically, we establish their completeness under appropriate norms, prove reflexivity under appropriate duality pairings, and demonstrate separability under mild conditions on the weight functions. As a pivotal application of our theoretical framework, we derive two robust existence theorems for solutions to the proposed model. These results not only extend classical partial differential equation theory to timescales but also provide a versatile tool for analysing dynamic systems with heterogeneous temporal domains. Full article

It is a well-known fact that the Dzhrbashyan–Nersesyan fractional derivative includes as particular cases the fractional derivatives of Riemann–Liouville, Gerasimov–Caputo, and Hilfer. The notion of resolving a family of operators for a linear equation with the Dzhrbashyan–Nersesyan fractional derivative is introduced here. Hille–Yosida-type theorem on necessary and sufficient conditions of the existence of a strongly continuous resolving family of operators is proved using Phillips-type approximations. The conditions concern the location of the resolvent set and estimates for the resolvent of a linear closed operator A at the unknown function in the equation. The existence of a resolving family means the existence of a solution for the equation under consideration. For such equation with an operator A satisfying Hille–Yosida-type conditions the uniqueness of a solution is shown also. The obtained results are illustrated by an example for an equation of the considered form in a Banach space of sequences. It is shown that such a problem in a space of sequences is equivalent to some initial boundary value problems for partial differential equations. Thus, this paper obtains key results that make it possible to determine the properties of the initial value problem involving the Dzhrbashyan–Nersesyan derivative by examining the properties of the operator in the equation; the results prove the existence and uniqueness of the solution and the correctness of the problem. Full article