Search Results (32)

This work develops an analytical framework for nonlinear fractional partial differential equations that combine Kirchhoff-type terms, double-phase operators, and $\psi$-Hilfer fractional derivatives. This paper investigates two classes of problems involving variable-exponent growth conditions. The first problem analyzes general nonlinear sources and formulates the solution as a fixed point of a nonlinear operator. Precisely, by proving that the functional energy is coercive, hemicontinuous, and strictly monotone, we establish the existence and the uniqueness of weak solutions via monotone operator theory. The second problem incorporates a convection-type nonlinearity, which breaks variational structure and requires the more robust theory of pseudomonotone operators. Under suitable growth and mixed-order assumptions on the nonlinearity, we prove the existence of at least one weak solution. The main tools are grounded in variable-exponent Lebesgue and Musielak–Orlicz–Sobolev spaces, with compact embeddings, modular estimates, and fractional integral identities playing a key role in the proofs. We note that the results contribute to the mathematical modeling of phenomena involving nonlocal elasticity, viscoelastic materials, phase-transition media, and fractional dynamical systems where the stiffness of the medium depends on the total deformation (Kirchhoff effect) and the energy density alternates between distinct growth regimes (double-phase). The $\psi$-Hilfer derivative enhances the scope by enabling models with tunable memory and hereditary effects. Full article

This paper investigates a new class of mixed impulsive fractional boundary value problems (BVPs) in which the mixing occurs both in the governing fractional differential equations—through the combined presence of $\psi$-Caputo and quantum (q-difference) fractional derivatives—and in the boundary conditions formulated via fractional integral constraints. By incorporating two distinct operators within the same dynamical framework, the proposed model is capable of capturing both memory effects and discrete-scale behaviors inherent in complex hybrid systems. Using the Banach contraction mapping principle and the Leray–Schauder nonlinear alternative, sufficient conditions ensuring the existence and uniqueness of solutions are established. The theoretical results unify and extend several known fractional models. Owing to its flexible structure, the proposed framework may serve as a useful mathematical tool for modeling impulsive phenomena in systems where non-local memory and scale-transition mechanisms coexist, such as in engineering, physics, and applied sciences. Finally, numerical examples are provided to illustrate the applicability and qualitative behavior of the solutions. Full article

In this paper, we investigate Turing instability and spatiotemporal pattern formation in a toxic-phytoplankton–zooplankton model incorporating Riesz fractional diffusion. By replacing classical Laplacians with fractional-order operators ${(-\Delta )}^{\varphi /2}$ and ${(-\Delta )}^{\psi /2}$, we establish a framework to capture species-specific anomalous diffusion in aquatic ecosystems. Theoretical analysis demonstrates that the fractional orders significantly modulate the Turing bifurcation threshold and the range of unstable modes. Numerical simulations, implemented via a DCT-based fractional finite difference scheme, reveal that: (1) fractional diffusion triggers pattern formation below the classical critical threshold, generating complex mixed structures unattainable in integer-order models; (2) the two fractional orders exert opposing influences on pattern morphology—decreasing the phytoplankton order $\varphi$ promotes a transition from stripes to hexagonal spots. Our results suggest that anomalous diffusion is a key mechanism for ecological pattern selection, providing new insights into the spatiotemporal complexity of plankton populations in heterogeneous environments. Full article

Let $\mathcal{A}$ be a unital ∗-algebra over the complex field $\mathbb{C}$, and let $\mathsf{\Psi }={\left\{{\psi }_m\right\}}_{m\in \mathbb{N}}$ be a nonlinear mixed bi-skew Jordan-type and skew Jordan higher derivation satisfies the relation ${\psi }_m(L_1\diamond L_2\diamond \dots \diamond L_{n-1}•L_n)={\displaystyle \sum _{r_1+\dots +r_n=m}}{\psi }_{r_1}(L_1)\diamond \dots \diamond {\psi }_{r_{n-1}}(L_{n-1})•{\psi }_{r_n}(L_n),$ where $L•N=LN+N{L}^{\ast }$ and $L\diamond N=L^{\ast }N+N^{\ast }L$ for all $L,N,L_i\in \mathcal{A}$ with $i\in \{1,2,\dots ,n\}$. We demonstrate that every such higher derivation $\mathsf{\Psi }={\left\{{\psi }_m\right\}}_{m\in \mathbb{N}}$ is an additive higher ∗-derivation. As an application, we use this result to characterize the structure of nonlinear mixed bi-skew Jordan-type and skew Jordan higher derivations on a class of typical unital ∗-algebras, including standard operator algebras and von Neumann factors. This result also generalizes several existing results, in particular those concerning nonlinear mixed bi-skew Jordan-type and skew Jordan derivations on unital ∗-algebras. Full article

This paper develops a generalized Laplace transform framework on weighted function spaces $C_{{\delta }_{\psi },\gamma }^n[a,b]$, establishing a symmetry between integer-order ${\delta }_{\psi }$ operators and fractional $\psi$-Hilfer derivatives at the level of transform representations. Explicit transformation formulas are derived for the nth-order ${\delta }_{\psi }$-derivative and the $\psi$-Hilfer fractional derivative of order $\alpha \in (m-1,m)$, with $m\le n$. These results form an analytical basis for the treatment of higher-order hybrid fractional Cauchy problems that systematically couple integer-order and fractional operators subject to mixed initial conditions. The general solution is expressed in closed form using a bivariate Mittag–Leffler function. To illustrate the utility of the approach, a representative second-order hybrid model is studied and compared numerically with its classical integer-order counterpart. The simulations reveal significant differences in the dynamical response, including variations in amplitude, damping behavior, and long-term evolution. Full article

This paper studies mixed impulsive boundary value problems involving tempered $\mathsf{\Psi }$-fractional derivatives of Caputo type. By introducing exponential tempering into the fractional framework, the proposed model effectively captures systems with fading memory—an improvement over conventional power-law kernels that assume long-range dependence. The generalized tempered $\mathsf{\Psi }$-operator unifies several existing fractional derivatives, offering enhanced flexibility for modeling complex dynamical phenomena. Impulsive effects and integral boundary conditions are incorporated to describe processes subject to sudden changes and historical dependence. The problem is reformulated as a Volterra integral equation, and fixed-point theory is employed to establish analytical results. Existence and uniqueness of solutions are proven using the Banach Contraction Mapping Principle, while the Leray–Schauder nonlinear alternative ensures existence in non-contractive cases. The proposed framework provides a rigorous analytical basis for modeling phenomena characterized by both fading memory and sudden perturbations, with potential applications in physics, control theory, population dynamics, and epidemiology. A numerical example is presented to illustrate the validity and applicability of the main theoretical results. Full article

Current analytical theories of recirculating flow in single-screw extruders consider only cross-channel flow in channels of infinite width with only one exception. Proper analysis of recirculating flow requires inclusion of normal velocities and the effect of finite channel width. More broadly, this paper presents an analytical description of lid-driven cavity flow—one of the most frequently studied flows in fluid dynamics. Expressions for velocities and flow rates for Newtonian fluids are obtained that satisfy the balance equations. These expressions have been compared to results of numerical analyses with good agreement. Flow rates and velocities are displayed with 3D surface plots and contour plots. These plots provide better insight into the flow behavior than 2D graphs. We have analyzed flow in slit channels with width much greater than the height ($W>>H$) and flow in a square channel ($W=H$). The vortex center (stagnation point) in a slit channel is located at normal coordinate $\psi =2/3$. The vortex center in a square channel is located at $\psi =0.76$. These analytical results allow for the development of better analytical models for melt temperature distribution, mixing, and devolatilization in single-screw extruders. Full article

The article is the result of the question mentioned in its title, namely, whether heat treatments without phase transformation and pressing of parts can improve the physicomechanical properties of metallic materials and alloys. Starting from this hypothesis, the article analyzes the influence of non-phase change thermal treatment TT and plastic deformation (compression) on a steel used for the realization of components in the engineering industry, as presented in the specific standards SR EN-10025 and SR EN-10027. The results of the tensile tests and of the Vickers hardness tests on the specimens made of this material are presented. The results in terms of material ultimate stress σ_u, yield strength S_y, elongation δ, reduction in cross section ψ, as well as those obtained in the Vickers test are summarized in tabular or graphical form. From the research conducted by the authors of this work, it can be seen that the 0.5 × T_m−s (T_m−s—melting-solidifying temperature, K) heat treatment gives the best mix of properties: mechanical strength similar to that of the non-treated material, improved elasticity and ductility, but with a small, negligible reduction in hardness. The results are useful to support the activities of optimal selection of heat treatments and plastic forming for various engineering applications. Heat treatment without phase transformation is essential for improving the mechanical properties of materials used in engineering. This study investigates the impact of heat treatments and plastic deformation on S355J2+N steel, highlighting the increase in yield strength and improvement in ductility. The results show an increase of up to 15% in yield strength and an improvement in relative elongation by 2% for treatments at 0.5 × T_m−s, while hardness remains almost unchanged. Full article

The $(k,\psi )$-fractional derivative based on the k-gamma function is a more general version of the Hilfer fractional derivative. It is widely used in differential equations to describe physical phenomena, population dynamics, and biological genetic memory problems. In this article, we mainly study the $4m+2$-point symmetric integral boundary value problem of nonlinear $(k,\psi )$-fractional differential coupled Laplacian equations. The existence and uniqueness of solutions are obtained by the Krasnosel’skii fixed-point theorem and Banach’s contraction mapping principle. Furthermore, we also apply the calculus inequality techniques to discuss the stability of this system. Finally, three interesting examples and numerical simulations are given to further verify the correctness and effectiveness of the conclusions. Full article

HIV is a lentivirus characterized by its cone shaped mature core. Visualization and structural examination of HIV requires the purification of virions to high concentrations. The yield and integrity of these virions are crucial for ensuring a uniform representation of all viral particles in subsequent analyses. In this study, we present a method for the purification of HIV virions which minimizes the forces applied to virions while maximizing the efficiency of collection. This method, which relies on virion sedimentation simulations, allows us to capture between 1000 and 5000 HIV virions released from individual HEK293 cells after transfection with the NL4.3 HIV backbone. We utilized this approach to investigate HIV core formation from several constructs: pNL4-3(RT:D₁₈₅A&D₁₈₆A) with an inactive reverse transcriptase, NL4.3(IN: V₁₆₅A&R₁₆₆A) with a type-II integrase mutation, and NL4.3(Ψ: Δ(105–278)&Δ(301–332)) featuring an edited Ψ packaging signal. Notably, virions from NL4.3(Ψ: Δ(105–278)&Δ(301–332)) displayed a mixed population, comprising immature virions, empty cores, and cores with detectable internal density. Conversely, virions derived from NL4.3(IN: V₁₆₅A&R₁₆₆A) exhibited a type II integrase mutant phenotype characterized by empty cores and RNP density localized around the cores, consistent with previous studies. In contrast, virions released from pNL4-3(RT:D₁₈₅A&D₁₈₆A) displayed mature cores containing detectable RNP density. We suggest that the sedimentation simulations developed in this study can facilitate the characterization of enveloped viruses. Full article

Soil salinization and alkalization can cause great losses to agricultural production in arid regions. Cotton, a common crop in arid and semi-arid regions in China, often encounters saline stress and alkaline stress. In this study, NaCl (8 g·kg⁻¹), Na₂CO₃ (8 g·kg⁻¹⁾, and a compound material (an organic polymer compound material) were mixed with field soil before cotton sowing, and the ion content, photosynthetic characteristics, and metabolite levels of the new cotton leaves were analyzed at the flowering and boll-forming stage, aiming to clarify the photosynthetic and metabolic mechanisms by which compound material regulates cotton’s tolerance to saline stress and alkaline stress. The results showed that the application of the compound material led to an increase in the K⁺/Na⁺ ratio, stomatal conductance (Gs), efficiency of PSII photochemistry (ψPSⅡ), potential activity (Fv/Fo), and chlorophyll content (Chla and Chlb), as well as the abundances of D-xylonic acid and DL-phenylalanine in the NaCl treatments. Additionally, there were increases in the K⁺ content, K⁺/Na⁺ ratio, Chla/b ratio, net photosynthetic rate (Pn), transpiration rate (Tr), ψPSⅡ, and D-saccharic acid abundance in the Na₂CO₃ treatments. A correlation analysis and a metabolic pathway analysis revealed that the compound material mainly regulated the photosynthetic characteristics of and the ion balance in the new leaves through regulating the abundance of key metabolites when the cotton was under NaCl stress or Na₂CO₃ stress. Furthermore, the positive impact of the compound material on the cotton’s NaCl stress tolerance was stronger than that on the cotton’s Na₂CO₃ stress tolerance. Full article

Leaf water potential ($\psi$_leaf) is a key indicator of plant water status, but its measurement is labor-intensive and limited in spatial coverage. While remote sensing has emerged as a useful tool for estimating vegetation water status, $\psi$_leaf remains unexplored, particularly in mixed forests. Here, we use spectral indices derived from unmanned aerial vehicle-based hyperspectral imaging and machine learning algorithms to assess $\psi$_leaf in a mixed, multi-species Mediterranean forest comprised of five key woody species: Pinus halepensis, Quercus calliprinos, Cupressus sempervirens, Ceratonia siliqua, and Pistacia lentiscus. Hyperspectral images (400–1000 nm) were acquired monthly over one year, concurrent with $\psi$_leaf measurements in each species. Twelve spectral indices and thousands of normalized difference spectral index (NDSI) combinations were evaluated. Three machine learning algorithms—random forest (RF), extreme gradient boosting (XGBoost), and support vector machine (SVM)—were used to model $\psi$_leaf. We compared the machine learning model results with linear models based on spectral indices and the NDSI. SVM, using species information as a feature, performed the best with a relatively good $\psi$_leaf assessment (R² = 0.53; RMSE = 0.67 MPa; rRMSE = 28%), especially considering the small seasonal variance in $\psi$_leaf ($\pm \sigma$ = 0.8 MPa). Predictions were best for Cupressus sempervirens (R² = 0.80) and Pistacia lentiscus (R² = 0.49), which had the largest $\psi$_leaf variances ($\pm \sigma$ > 1 MPa). Aggregating data at the plot scale in a ‘general’ model markedly improved the $\psi$_leaf model (R² = 0.79, RMSE = 0.31 MPa; rRMSE = 13%), providing a promising tool for monitoring mixed forest $\psi$_leaf. The fact that a non-species-specific, ‘general’ model could predict $\psi$_leaf implies that such a model can also be used with coarser resolution satellite data. Our study demonstrates the potential of combining hyperspectral imagery with machine learning for non-invasive $\psi$_leaf estimation in mixed forests while highlighting challenges in capturing interspecies variability. Full article

This research is concerned with the existence and uniqueness of solutions for a coupled system of $\Psi$–Riemann–Liouville fractional differential equations. To achieve this objective, we establish a set of necessary conditions by formulating the problem as an integral equation and utilizing well-known fixed-point theorems. By employing these mathematical tools, we demonstrate the existence and uniqueness of solutions for the proposed system. Additionally, to illustrate the practical implications of our findings, we provide several examples that showcase the main results obtained in this study. Full article

Glyphosate is the most used herbicide in agriculture. Its major metabolite is AMPA (aminomethylphosphonic acid), but N-acetyl-AMPA and N-acetylglyphosate are also metabolites of interest. For risk assessment, a general residue definition was proposed as the sum of glyphosate, AMPA, N-acetyl-glyphosate and N-acetyl-AMPA, expressed as glyphosate. A confirmatory method for glyphosate in fat, liver and kidneys, as well as a confirmatory method for AMPA and N-acetyl-glyphosate in all matrices, are still missing. In this paper, we present a method for the quantitative determination of glyphosate residues and its metabolites AMPA, N-acetyl-AMPA and N-acetyl-glyphosate by liquid chromatography–mass spectrometry (LC-MS/MS) in adipose tissue, liver, eggs, milk and honey without derivatization. Different chromatographic columns were tested, with the Hypercarb column providing the best results. The analytes were eluted with mobile phases of acidified water with 1.2% formic acid and 0.5% formic acid in acetonitrile. Sample purification procedures were also optimized by varying the solvent extraction mixtures (water, methanol and mixture ψ (methanol, water) = 1:1, each with the addition of 1% formic acid (v/v)), using different sorbents in solid phase extraction (SPE) (polymeric cationic (PCX) and anionic (PAX)) and using dispersive solid phase extraction (dSPE) (C18 and PSA) by modifying the extraction procedures. Finally, the analytes were extracted from the samples with 1% formic acid in water (v/v). Milk and adipose tissue were purified by the addition of dichloromethane, while liver and egg samples were purified by SPE with a mixed cation exchange sorbent and ultrafiltration with cut-off filters. The proposed analytical procedures were validated according to SANTE/11312/2021 guidelines: linearity, limits of quantification, precision and accuracy were determined for all matrices. The limits of quantification (LOQs) ranged from 0.025 to 0.2 mg kg⁻¹. Precision, expressed as relative standard deviation, was <20%, while accuracy, expressed as analytical recovery, ranged from 70% to 120%. During method validation, the measurement uncertainty was estimated to be <50% for all analytes. Good validation parameters according to the SANTE document were achieved for all analytes. Therefore, the method can be considered reliable and sensitive enough for routine monitoring of polar pesticides. The application of the accredited method in routine analysis will provide data that are useful for the re-evaluation of risk assessment studies in foods of animal origin. Full article