Search Results (18)

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

In this article, we delve into delayed fractional differential equations with Riemann–Stieltjes integral boundary conditions and fractional impulses. By using differential inequality techniques and some fixed-point theorems, some novel sufficient assessments for convenient verification have been devised to ensure the existence and uniqueness of solutions. We further employ the nonlinear analysis to reveal that this problem is Ulam–Hyers (UH) stable. Finally, some examples and numerical simulations are presented to illustrate the reliability and validity of our main results. Full article

The Hadamard fractional derivative and integral are important parts of fractional calculus which have been widely used in engineering, biology, neural networks, control theory, and so on. In addition, the periodic boundary conditions are an important class of symmetric two-point boundary conditions for differential equations and have wide applications. Therefore, this article considers a class of nonlinear Hadamard fractional coupling $(p_1,p_2)$-Laplacian systems with periodic boundary value conditions. Based on nonlinear analysis methods and the contraction mapping principle, we obtain some new and easily verifiable sufficient criteria for the existence and uniqueness of solutions to this system. Moreover, we further discuss the generalized Ulam–Hyers (GUH) stability of this problem by using some inequality techniques. Finally, three examples and simulations explain the correctness and availability of our main results. Full article

To produce functional protective textiles with minimal environmental footprints, we developed durable superhydrophobic antimicrobial textiles. These textiles are characterized by a micro-pleated structure on polyester fiber surfaces, achieved through a novel plasma impregnation crosslinking process. This process involved the use of water as the dispersion medium, water-soluble nanosilver monomers for antimicrobial efficacy, fluorine-free polydimethylsiloxane (PDMS) for hydrophobicity, and polyester (PET) fabric as the base material. The altered surface properties of these fabrics were extensively analyzed using scanning electron microscopy (SEM), Fourier transform infrared spectroscopy (FTIR), X-ray photoelectron spectrometry (XPS), thermogravimetric analysis (TGA), and water contact angle (WCA) measurements. The antimicrobial performance of the strains was evaluated using Gram-negative Escherichia coli and Gram-positive Staphylococcus aureus. After treatment, the fabrics exhibited enhanced hydrophobic and antimicrobial properties, which was attributed to the presence of a micro-pleated structure and nanosilver. The modified textiles demonstrated a static WCA of approximately 154° and an impressive 99.99% inhibition rate against both test microbes. Notably, the WCA remained above 140° even after 500 washing cycles or 3000 friction cycles. Full article

The Langevin equation is a model for describing Brownian motion, while the Sturm–Liouville equation is an important mechanical model. This paper focuses on the solvability and stability of nonlinear impulsive Langevin and Sturm–Liouville equations with Caputo–Hadamard (CH) fractional derivatives and multipoint boundary value conditions. To unify the two types of equations, we investigate a general nonlinear impulsive coupled implicit system. By cleverly constructing relevant operators involving impulsive terms, we establish the coincidence degree theory and obtain the solvability. We explore the stability of solutions using nonlinear analysis and inequality techniques. As the most direct application, we naturally obtained the solvability and stability of the Langevin and Sturm–Liouville equations mentioned above. Finally, an example is provided to demonstrate the validity and availability of our major findings. Full article

Gallium nitride high-electron-mobility transistor (GaN HEMT) power devices are favored in various scenarios due to their high-power density and efficiency. However, with the significant increase in the heat flux density, the junction temperature of GaN HEMT has become a crucial factor in device reliability. Since the junction temperature monitoring technology for GaN HEMT based on temperature-sensitive electrical parameters (TSEPs) is still in the exploratory stage, the TSEPs’ characteristics of GaN HEMT have not been definitively established. In this paper, for the common steady-state TSEPs of GaN HEMT, the variation rules of the saturation voltage with low current injection, threshold voltage, and body-like diode voltage drop with temperature are investigated. The influences on the three TSEPs’ characteristics are considered, and their stability is discussed. Through experimental comparison, it is found that the saturation voltage with low current injection retains favorable temperature-sensitive characteristics, which has potential application value in junction temperature measurement. However, the threshold voltage as a TSEP for certain GaN HEMT is not ideal in terms of linearity and stability. Full article

The fractional order $\mathcal{p}$-Laplacian differential equation model is a powerful tool for describing turbulent problems in porous viscoelastic media. The study of such models helps to reveal the dynamic behavior of turbulence. Therefore, this article is mainly concerned with the periodic boundary value problem (BVP) for a class of nonlinear Hadamard fractional differential equation with $\mathcal{p}$-Laplacian operator. By virtue of an important fixed point theorem on a complete metric space with two distances, we study the solvability and approximation of this BVP. Based on nonlinear analysis methods, we further discuss the generalized Ulam-Hyers (GUH) stability of this problem. Eventually, we supply two example and simulations to verify the correctness and availability of our main results. Compared to many previous studies, our approach enables the solution of the system to exist in metric space rather than normed space. In summary, we obtain some sufficient conditions for the existence, uniqueness, and stability of solutions in the metric space. Full article

The Ayala-Gilpin (AG) kinetics system is one of the famous mathematical models of ecosystem. This model has been widely concerned and studied since it was proposed. This paper stresses on a nonlinear distributed delayed periodic AG-ecosystem with competition on time scales. In the sense of time scale, our model unifies and generalizes the discrete and continuous cases. Firstly, with the aid of the auxiliary function having only two zeros in the real number field, we apply inequality technique and coincidence degree theory to obtain some sufficient criteria which ensure that this model has periodic solutions on time scales. Meanwhile, the global asymptotic stability of the periodic solution is founded by employing stability theory in the sense of Lyapunov. Eventually, we provide an illustrative example and conduct numerical simulation by means of MATLAB tools. Full article

Based on the second derivative, this paper directly establishes the coincidence degree theory of a nonlinear periodic Sturm–Liouville (SL) system. As applications, we study the existence of periodic solutions to the S–L system with some special nonlinear functions by applying Mawhin’s continuation theorem. Some examples and simulations are furnished to inspect the correctness and availability of the chief findings. Full article

The Langevin system is an important mathematical model to describe Brownian motion. The research shows that fractional differential equations have more advantages in viscoelasticity. The exploration of fractional Langevin system dynamics is novel and valuable. Compared with the fractional system of Caputo or Riemann–Liouville (RL) derivatives, the system with Mittag–Leffler (ML)-type fractional derivatives can eliminate singularity such that the solution of the system has better analytical properties. Therefore, we concentrate on a nonlinear Langevin system of ML-type fractional derivatives affected by time-varying delays and differential feedback control in the manuscript. We first utilize two fixed-point theorems proposed by Krasnoselskii and Schauder to investigate the existence of a solution. Next, we employ the contraction mapping principle and nonlinear analysis to establish the stability of types such as Ulam–Hyers (UH) and Ulam–Hyers–Rassias (UHR) as well as generalized UH and UHR. Lastly, the theoretical analysis and numerical simulation of some interesting examples are carried out by using our main results and the DDESD toolbox of MATLAB. Full article

We establish a non-linear diffusion partial differential equation (PDE) model to depict the dynamic mechanism of Internet gaming disorder (IGD). By constructing appropriate super- and sub-solutions and applying Schauder’s fixed point theorem and continuation method, we study the existence and asymptotic stability of traveling wave solutions to probe into the oscillating behavior of IGD. An example is numerically simulated to examine the correctness of our outcomes. Full article

Pancreatic ductal adenocarcinoma (PDAC) is one of the highest mortalities malignant tumors, which is characterized by difficult diagnosis, rapid progression and high recurrence rate. Nevertheless, PDAC responds poorly to conventional therapies, which highlights the urgency to identify novel prognostic and therapeutic targets. LEMT2 was a newly discovered protein-encoding gene with little cancer research and an unclear mechanism. Thus, this study aimed to illustrate LETM2 as the crucial oncogene for tumor progression in PDAC. In this study, we analyzed the expression level and prognostic value of LETM2 in multiple cancers using pan-cancer analysis. The analyses based on the TCGA-GTEx dataset indicated that the LETM2 expression was obviously elevated in several cancers, and it was the most significantly related to the dismal prognosis of PDAC. Subsequently, we demonstrated the functional role and mechanism of LETM2 by clinical sample evaluation, and in in vitro and in vivo experiments. Immunohistochemical analyses showed that high expression of LETM2 was correlated with poor outcomes of PDAC. Moreover, we demonstrated that LETM2 knockdown significantly inhibited tumor proliferation and metastasis, and promoted cell apoptosis, while LETM2 overexpression exerted the opposite effects. Finally, the impairment caused by LETM2-knockdown could be recovered via excitation of the PI3k-Akt pathway in vitro and in vivo animal models, which suggested that LETM2 could activate the downstream PI3K-Akt pathway to participate in PDAC progression. In conclusion, the study enhanced our understanding of LETM2 as an oncogene hallmark of PDAC. LETM2 may facilitate tumor progression by activating the PI3K-Akt signaling pathway, which provides potential targets for the diagnosis, treatment, and prognosis of pancreatic cancer. Full article

The fractional Langevin equation is a very effective mathematical model for depicting the random motion of particles in complex viscous elastic liquids. This manuscript is mainly concerned with a class of nonlinear fractional Langevin equations involving nonsingular Mittag–Leffler (ML) kernel. We first investigate the existence and uniqueness of the solution by employing some fixed-point theorems. Then, we apply direct analysis to obtain the Ulam–Hyers (UH) type stability. Finally, the theoretical analysis and numerical simulation of some interesting examples show that there is a great difference between the fractional Langevin equation and integer Langevin equation in describing the random motion of free particles. Full article

The fractional Langevin equation has more advantages than its classical equation in representing the random motion of Brownian particles in complex viscoelastic fluid. The Mittag–Leffler (ML) fractional equation without singularity is more accurate and effective than Riemann–Caputo (RC) and Riemann–Liouville (RL) fractional equation in portraying Brownian motion. This paper focuses on a nonlinear ML-fractional Langevin system with distributed lag and integral control. Employing the fixed-point theorem of generalised metric space established by Diaz and Margolis, we built the Hyers–Ulam–Rassias (HUR) stability along with Hyers–Ulam (HU) stability of this ML-fractional Langevin system. Applying our main results and MATLAB software, we have carried out theoretical analysis and numerical simulation on an example. By comparing with the numerical simulation of the corresponding classical Langevin system, it can be seen that the ML-fractional Langevin system can better reflect the stationarity of random particles in the statistical sense. Full article

SiC/MoSi₂-SiC-Si coatings for nuclear graphite spheres with different Si-Mo ratios were prepared through two-step pack cementation. XRD, SEM and EDS techniques were used to analyze the composition and microstructure of the coatings. The oxidation resistance performance of the composites at 1773 K, in static air, was investigated. The results showed that the SiC-MoSi₂-Si coating could be divided into a denser inner layer and a loose outer layer, as free Si would infiltrate into the inner micropores of the coating under capillary force. When the Si/Mo ratio of the second pack cementation was 7:1, the thickness of the denser inner layer basically reached the maximum and exhibited excellent oxidation resistance ability, with a weight gain of 0.19% after 200 h oxidation. The performance improvement was analyzed as a result of the addition of SiC and C powder in the pack cementation process, effectively increasing the phase interfaces to relax the thermal stress in the coating. With different Si-Mo ratios, the content of residual Si and the formation rate of SiO₂ glass layer on the coating surface were also different, thus affecting the anti-oxidation performance. The main reactions occurring at different stages of the oxidation curve were also discussed. Full article