Search

Abstract To quantitatively assess the diagnostic efficacy of multiple parameters derived from multi-b-value diffusion-weighted imaging (DWI) using turbo spin echo (TSE)–based acquisition techniques in patients with solitary pulmonary lesions (SPLs). A total of 105 patients with SPLs underwent lung DWI using single-shot TSE–based acquisition techniques and multiple b values. The apparent diffusion coefficient (ADC), intravoxel incoherent motion (IVIM) parameters, and lesion-to-spinal cord signal intensity ratio (LSR), were analyzed to compare the benign and malignant groups using the Mann–Whitney U test and receiver operating characteristic analysis. The Dstar values observed in lung cancer were slightly lower than those observed in pulmonary benign lesions (28.164 ± 31.950 versus 32.917 ± 34.184; Z = -2.239, p = 0.025). The LSR values were significantly higher in lung cancer than in benign lesions (1.137 ± 0.581 versus 0.614 ± 0.442; Z = − 4.522, p

Background: Oxidative stress (OS) is involved in the development of diabetes, but the genetic mechanisms are not completely understood. We integrated multi-omics data in order to explore the genetic relations between OS-related genes, diabetes mellitus, and microvascular complications using Mendelian randomization and colocalization analysis. Methods: Summary-level data related to OS were acquired from respective studies of methylation, expression, and protein abundance quantitative trait loci. Genetic associations concerning diabetes, diabetic nephropathy (DN), and diabetic retinopathy (DR) were derived from the FinnGen study. Summary-data-based Mendelian randomization (SMR) analysis was conducted to evaluate the correlations between molecular features concerned with OS-related genes and diabetes mellitus, along with its microvascular complications. Additionally, we performed colocalization analysis to determine if the detected signal pairs shared a causal genetic variant. Results: At the genetic level, we identified ten potential causal associations of oxidative stress genes with diabetes, along with microvascular complications, through SMR and colocalization analysis. After integrating the DNA methylation quantitative trait loci (mQTL) and expression QTL (eQTL) data, our analyses revealed a correlation between the methylation site cg26343298 and reduced expression of TP53INP1, supporting the protective role of cg26343298 methylation on type 2 diabetes (T2D) and diabetic nephropathy. Similarly, an inverse association was observed between gene methylation and expression in CHEK1 (cg07110182), confirming the beneficial effect of modification of CHEK1 by cg07110182 in diabetic retinopathy. In addition, upregulation of SUOX expression by cg22580629 was linked to a reduced risk of diabetic retinopathy. At circulating protein levels, genetically predicted a higher level of ICAM1 (OR 1.05, 95%CI 1.03–1.08) was positively connected with the risk of diabetic retinopathy. Conclusions: This SMR study elucidated that the TP53INP1 gene was putatively associated with T2D and DN risk, while the SUOX and CHEK1 genes were associated with DR risk through oxidative stress mechanisms. Additionally, our study showed a positive correlation between the ICAM-1 protein and DR. These findings may enhance our understanding of their pathogenesis and suggest new therapeutic targets for clinical practice.

Unmanned Aerial Vehicle (UAV) has very wide application prospect in aiding terrestrial cellular network communication, but it remains a challenge to optimize UAV locations and maximize user service rate during deployment. In this paper, a novel network optimization scheme based on anti-flocking model and improved Nash Equilibrium (NE) algorithm is proposed by studying the problem of dynamic UAV deployment and backhaul transmission. Firstly, the UAV-adaptive algorithm based on gray wolf optimization (U-GWO) is used to predeploy UAVs with limited number of UAVs. Secondly, ground mobile users are tracked by building a UAV-based anti-flocking (U-AF) model. Then, during the tracking of ground users by UAV, an improved NE strategy is used to establish the backhaul transmission links between UAVs, ground BSs and other UAVs to ensure that deployed UAVs can maximize the service rate and effective backhaul transmission rate of ground users. Simulation results show that the average service rate of User Equipment (UE) with U-GWO algorithm is improved from 1 % to 5.77 % compared to other different swarm intelligence optimization algorithms. And the service rate obtained with U-AF algorithm is 43.2 % improved compared to the baseline scenario without U-AF algorithm. For UAV backhaul transmission link construction, the simulation results show that the proposed improved NE strategy improves the average effective backhaul transmission rate by 12 %, the minimum backhaul transmission rate by 84 % and the overall iteration number by 5 % on average compared to a pure NE strategy.

This paper discusses the S-asymptotically periodic problem of fractional evolution equation with delay. By introducing a new noncompact measure theory involving infinite interval, we study the existence of S-asymptotically periodic mild solutions under the situation that the relevant semigroup is noncompact and the nonlinear term satisfies more general growth conditions instead of Lipschitz-type conditions. Moreover, by establishing a new Gronwall-type integral inequality corresponding to fractional differential equation with delay, we consider the global asymptotic behavior of S-asymptotically periodic mild solutions, which will make up for the blank of this field.

In this paper, we investigate an initial value problem for a nonlinear fractional differential equation on an infinite interval. The differential operator is taken in the Hadamard sense and the nonlinear term involves two lower-order fractional derivatives of the unknown function. In order to establish the global existence criteria, we first verify that there exists a unique positive solution to an integral equation based on a class of new integral inequality. Next, we construct a locally convex space, which is metrizable and complete. On this space, applying Schäuder’s fixed point theorem, we obtain the existence of at least one solution to the initial value problem.

This research work is dedicated to an investigation for a new kind of boundary value problem of nonlinear fractional differential equation supplemented with general boundary condition. A full analysis of existence and uniqueness of positive solutions is respectively proved by Leray–Schauder nonlinear alternative theorem and Boyd–Wong’s contraction principles. Furthermore, we prove the Hyers–Ulam (HU) stability and Hyers–Ulam–Rassias (HUR) stability of solutions. An example illustrating the validity of the existence result is also discussed.

In this paper, the maximal and minimal iterative positive solutions are investigated for a singular Hadamard fractional differential equation boundary value problem with a boundary condition involving values at infinite number of points. Green's function is deduced and some properties of Green's function are given. Based upon these properties, iterative schemes are established for approximating the maximal and minimal positive solutions.

Abstract A Kirchhoff-type problem with concave-convex nonlinearities is studied. By constrained variational methods on a Nehari manifold, we prove that this problem has a sign-changing solution with least energy. Moreover, we show that the energy level of this sign-changing solution is strictly larger than the double energy level of the ground state solution.

Abstract In this paper, we consider the initial boundary value problem for a class of nonlinear fractional partial integro-differential equations of mixed type with non-instantaneous impulses in Banach spaces. Sufficient conditions of existence and uniqueness of PC-mild solutions for the equations are obtained via general Banach contraction mapping principle, Krasnoselskii’s fixed point theorem, and α-order solution operator.

Abstract In this work, the aim is to discuss a new class of singular nonlinear higher-order fractional boundary value problems involving multiple Riemann–Liouville fractional derivatives. The boundary conditions are constituted by Riemann–Stieltjes integral boundary conditions. The existence and multiplicity of positive solutions are derived via employing the Guo–Krasnosel’skii fixed point theorem. In addition, the main results are demonstrated by some examples to show their validity.

Abstract This paper focuses on a class of hider-order nonlinear fractional boundary value problems. The boundary conditions contain Riemann–Stieltjes integral and nonlocal multipoint boundary conditions. It is worth mentioning that the nonlinear term and the boundary conditions contain fractional derivatives of different orders. Based on the Schauder fixed point theorem, we obtain the existence of solutions under the hypothesis that the nonlinear term satisfies the Carathéodory conditions. We apply the Banach contraction mapping principle to obtain the uniqueness of solutions. Moreover, by using the theory of spectral radius we prove the uniqueness and nonexistence of positive solutions. Finally, we illustrate our main results by some examples.

Abstract We consider the existence of solutions for the following Hadamard-type fractional differential equations: { D α H u ( t ) + q ( t ) f ( t , u ( t ) , H D β 1 u ( t ) , H D β 2 u ( t ) ) = 0 , 1 < t < + ∞ , u ( 1 ) = 0 , D α − 2 H u ( 1 ) = ∫ 1 + ∞ g 1 ( s ) u ( s ) d s s , D α − 1 H u ( + ∞ ) = ∫ 1 + ∞ g 2 ( s ) u ( s ) d s s , $$ \textstyle\begin{cases} {}^{H}D^{\alpha }u(t)+q(t)f(t,u(t), {}^{H}D^{\beta _{1}}u(t),{}^{H}D^{ \beta _{2}}u(t))=0,\quad 1< t< +\infty , \\ u(1)=0, \\ {}^{H}D^{\alpha -2}u(1)=\int ^{+\infty }_{1}g_{1}(s)u(s)\frac{ds}{s}, \\ {}^{H}D^{\alpha -1}u(+\infty )=\int ^{+\infty }_{1}g_{2}(s)u(s) \frac{ds}{s}, \end{cases} $$ where 2 < α ≤ 3 $2

Based on properties of Green’s function and by Avery–Peterson fixed point theorem, the existence of multiple positive solutions are obtained for singular p-Laplacian fractional differential equation with infinite-point boundary conditions, and an example is given to demonstrate the validity of our main results.

In this article, by using the Schauder fixed point theorem, we first study the existence of solutions for a new coupled system of Caputo fractional differential equations with multipoint boundary value conditions under the assumption that the nonlinear term satisfies two types of the Carathéodory conditions. Using this result, we provide the existence of solutions of the system with infinite points and Riemann–Stieltjes integral boundary conditions, respectively, instead of doing it directly. Finally, we give three examples to illustrate the feasibility of main results.

We begin by introducing some function spaces Lcp(R+),Xcp(J) made up of integrable functions with exponent or power weights defined on infinite intervals, and then we investigate the properties of Mellin convolution operators mapping on these spaces, next, we derive some new boundedness and continuity properties of Hadamard integral operators mapping on Xcp(J) and Xp(J). Based on this, we investigate a class of boundary value problems for Hadamard fractional differential equations with the integral boundary conditions and the disturbance parameters, and obtain uniqueness results for positive solutions to the boundary value problem under some weaker conditions.

In this paper, we discuss the asymptotically periodic problem for the abstract fractional evolution equation under order conditions and growth conditions. Without assuming the existence of upper and lower solutions, some new results on the existence of the positive S-asymptotically ω-periodic mild solutions are obtained by using monotone iterative method and fixed point theorem. It is worth noting that Lipschitz condition is no longer needed, which makes our results more widely applicable.

In this paper, we establish the results of multiple solutions for a class of modified nonlinear Schrödinger equation involving the p-Laplacian. The main tools used for analysis are the critical points theorems by Ricceri and the dual approach.

Abstract By using the method of mixed monotone operator, a unique positive solution is obtained for a singular p-Laplacian boundary value system with infinite-point boundary conditions in this paper. Green’s function is derived and some useful properties of the Green’s function are obtained. Based upon these new properties and by using mixed monotone operator, the existence results of the positive solutions for the boundary value problem are established. Moreover, the unique positive solution that we obtained in this paper is dependent on λ,μ $\lambda ,\mu $, and an iterative sequence and convergence rate, which are important for practical application, are given. An example is given to demonstrate the application of our main results.

Abstract In this paper, we consider a new class of singular nonlinear higher order fractional boundary value problems supplemented with sum of Riemann–Stieltjes integral type and nonlocal infinite-point discrete type boundary conditions. The fractional derivative of different orders is involved in the nonlinear terms and boundary conditions, and the nonlinear terms are allowed to be singular in regard to not only time variable but also space variables. A unique positive solution is established by using the fixed point theorem of mixed monotone operator. In addition, some significant properties of the unique solution depending on the parameter λ are stated. In the end, two examples are worked out to illustrate our main results.

Abstract In this paper, we focus on a generalized singular fractional order Kelvin–Voigt model with a nonlinear operator. By using analytic techniques, the uniqueness of solution and an iterative scheme converging to the unique solution are established, which are very helpful to govern the process of the Kelvin–Voigt model. At the same time, the corresponding eigenvalue problem is studied and the property of solution for the eigenvalue problem is established. Some examples are given to illuminate the main results.

Abstract In this paper, by employing fixed point theory, we investigate the existence and uniqueness of solutions for a class of nonlinear fractional integro-differential equations on semi-infinite domains in a Banach space.

An input vector composed of various features plays an important role in short-term traffic forecasting. However, there is limited research on the optimal feature selection of an input vector for a certain forecasting task. To fill the gap, this paper proposes a cohesion-based heuristic feature selection method by analyzing the nature of the forecasting methods. This method is able to determine which features should be contained in an input vector to make a forecasting algorithm perform better. The proposed method is demonstrated in two experiments based on the empirical traffic flow data. The results show that the method is able to improve the performances of the short-term traffic forecasting algorithms. It is then suggested to consider the proposed method as a preprocessing procedure in practical forecasting applications.

Abstract In this paper, we study the initial boundary value problem for a Petrovsky type equation with a memory term, nonlinear weak damping, and a superlinear source: utt+Δ2u−∫0tg(t−τ)Δ2u(τ)dτ+|ut|m−2ut=|u|p−2u,in Ω×(0,T). $$ u_{tt}+\Delta ^{2} u- \int _{0}^{t} g(t-\tau )\Delta ^{2} u(\tau )\,\mathrm{d} \tau + \vert u_{t} \vert ^{m-2}u_{t}= \vert u \vert ^{p-2}u,\quad \text{in }\varOmega \times (0,T). $$ When the source is stronger than dissipations, we obtain the existence of certain weak solutions which blow up in finite time with initial energy E(0)=R $E(0)=R$ for any given R≥0 $R\geq 0$.

In this paper, we study a system of Hadamard fractional multi-point boundary value problems. We first obtain triple positive solutions when the nonlinearities satisfy some bounded conditions. Next, we also obtain a nontrivial solution when the nonlinearities can be asymptotically linear growth. Furthermore, we provide two examples to illustrate our main results.

Background Minxian black fur (MBF) sheep are found in the northwestern parts of China. These sheep have developed several special traits. Skin color is a phenotype subject to strong natural selection and diverse skin colors are likely a consequence of differences in gene regulation. Methods Skin structure, color differences, and gene expression (determined by RNA sequencing) were evaluated the Minxian black fur and Small-tail Han sheep (n = 3 each group), which are both native Chinese sheep breeds. Results Small-tail Han sheep have a thicker skin and dermis than the Minxian black fur sheep (P

In this paper, we study the solvability and asymptotic properties of a recently derived gyre model of nonlinear elliptic Schrödinger equation arising from the geophysical fluid flows. The existence theorems and the asymptotic properties for radial positive solutions are established due to space theory and analytical techniques, some special cases and specific examples are also given to describe the applicability of model in gyres of geophysical fluid flows.

In this paper, we consider the iterative algorithm for a boundary value problem of n-order fractional differential equation with mixed integral and multipoint boundary conditions. Using an iterative technique, we derive an existence result of the uniqueness of the positive solution, then construct the iterative scheme to approximate the positive solution of the equation, and further establish some numerical results on the estimation of the convergence rate and the approximation error.

In this paper, we consider the Cauchy problem for the 2D inviscid Boussinesq equations with N being the buoyancy frequency. It is proved that for general initial data u0∈Hs with s>3, the life span of the classical solutions satisfies T>Cln N3/4.

By sequential techniques and mixed monotone operator, the uniqueness of positive solution for singular p-Laplacian fractional differential system with infinite-point boundary conditions is obtained. Green's function is derived, and some useful properties of Green' function are obtained. Based on these new properties, the existence of unique positive solutions is established, moreover, an iterative sequence and a convergence rate are given, which are important for practical application, and an example is given to demonstrate the validity of our main results.

In this paper, we establish the results of nonexistence and existence of blow-up radial solutions for a k-Hessian equation with a nonlinear operator. Under some suitable growth conditions for nonlinearity, the result of nonexistence of blow-up solutions is established, a sufficient and necessary condition on existence of blow-up solutions is given, and some further results are obtained.

In this paper, we study a class of nonlinear singular system with coupled integral boundary condition. Based on the Guo–Krasnosel'skii fixed point theorem, some new results on the existence of symmetric positive solutions for the coupled singular system are obtained. The impact of the two different parameters on the existence of symmetric positive solutions is also investigated. Finally, an example is then given to demonstrate the applicability of our results.

Abstract In this paper, we focus on the existence and asymptotic analysis of positive solutions for a class of singular fractional differential equations subject to nonlocal boundary conditions. By constructing suitable upper and lower solutions and employing Schauder’s fixed point theorem, the conditions for the existence of positive solutions are established and the asymptotic analysis for the obtained solution is carried out. In our work, the nonlinear function involved in the equation not only contains fractional derivatives of unknown functions but also has a stronger singularity at some points of the time and space variables.

Abstract This paper studies a system of fractional differential equations with Riemann–Stieltjes integral conditions. The existence and uniqueness of nontrivial solutions to the above system are established under some weaker conditions by the Leray–Schauder topological degree. Two examples are set up to testify the validity of the main results.

Abstract In this paper, we study periodic boundary value problems of fractional semilinear integro-differential equations with non-instantaneous impulses in Banach spaces. By the measure of noncompactness, the theory of β-resolvent family, and the fixed point theorem, we obtain several sufficient conditions on the existence of mild solutions for such problems. Finally, an example is given to show the main results of this paper.

Abstract In this paper, we consider a class of fractional differential equations with infinite-point boundary value conditions. Under some conditions concerning the spectral radius with respect to the relevant linear operator, both the existence of uniqueness and the nonexistence of positive solution are obtained by means of the iterative technique.

In this article, we focus on the existence of infinitely many weak solutions for the modified nonlinear Schrodinger equation $$ -\Delta u+V(x) u-[\Delta(1+u^2)^{\alpha/2}]\frac{\alpha u}{2(1+u^2) ^{\frac{2-\alpha}2}}=f(x,u),\quad \text{in } \mathbb{R}^N, $$ where $1\leq\alpha

Abstract In this article, we first establish an existence and uniqueness result for a class of systems of nonlinear operator equations under more general conditions by means of the cone theory and monotone iterative technique. Furthermore, the iterative sequence of the solution and the error estimation of the system are given. Then we use this new result to study the existence and uniqueness of the solution for boundary value problems of systems of fractional differential equations with a Riemann–Stieltjes integral boundary condition in real Banach spaces. The results obtained in this paper are more general than many previous results and complement them.

Abstract In this paper, we focus on the convergence analysis and error estimation for the unique solution of a p-Laplacian fractional differential equation with singular decreasing nonlinearity. By introducing a double iterative technique, in the case of the nonlinearity with singularity at time and space variables, the unique positive solution to the problem is established. Then, from the developed iterative technique, the sequences converging uniformly to the unique solution are formulated, and the estimates of the error and the convergence rate are derived.

Abstract This paper is concerned with the uniqueness of positive solutions for a class of singular fractional differential equations with integral boundary conditions. The nonlinear term and boundary conditions of fractional differential equation contain the fractional order derivatives. The uniqueness of positive solutions is derived by the fixed point theorem of mixed monotone operator. An example is given to demonstrate the validity of our main results.

This paper deals with the study of the existence of positive solutions for a class of nonlinear higher-order fractional differential equations in which the nonlinear term contains multi-term lower-order derivatives. By reducing the order of the highest derivative, the higher-order fractional differential equation is transformed into a lower-order fractional differential equation. Then, combining with the properties of left-sided Riemann–Liouville integral operators, we obtain the existence of the positive solutions of fractional differential equations utilizing some weaker conditions. Furthermore, some examples are given to demonstrate the validity of our main results.

Abstract In this paper, we investigate the existence of positive solutions for a system of nonlinear fractional differential equations nonlocal boundary value problems with parameters and p-Laplacian operator. Under different combinations of superlinearity and sublinearity of the nonlinearities, various existence results for positive solutions are derived in terms of different values of parameters via the Guo-Krasnosel’skii fixed point theorem.

Abstract In this paper, we are concerned with the existence and uniqueness of solutions for impulsive fractional integro-differential equation of mixed type with constant coefficient and antiperiodic boundary condition. Our results are based on the Banach contraction mapping principle and the Krasnoselskii fixed point theorem. Some examples are also given to illustrate our results.

Abstract This paper focuses on the maximum and minimum solutions for a fractional order differential system, involving a p-Laplacian operator and nonlocal boundary conditions, which arises from many complex processes such as ecological economy phenomena and diffusive interaction. By introducing new type growth conditions and using the monotone iterative technique, some new results about the existence of maximal and minimal solutions for a fractional order differential system is established, and the estimation of the lower and upper bounds of the maximum and minimum solutions is also derived. In addition, the iterative schemes starting from some explicit initial values and converging to the exact maximum and minimum solutions are also constructed.

In this paper, we investigate the existence of at least three positive solutions to a singular boundary value problem of Caputo's fractional differential equations with a boundary condition involving values at infinite number of points. Firstly, we establish Green's function and its properties. Then, the existence of multiple positive solutions is obtained by Avery–Peterson's fixed point theorem. Finally, an example is given to demonstrate the application of our main results.

The existence of maximal and minimal positive solutions for singular infinite-point p-Laplacian fractional differential equation is investigated in this paper. Green's function is derived, and some properties of Green's function are obtained. Based upon these properties of Green's function, the existence of maximal and minimal positive solutions is obtained, and iterative schemes are established for approximating the maximal and minimal positive solutions.

In this paper, we study a higher-order fractional differential equation with integral boundary conditions and a parameter. Under different conditions of nonlinearity, existence and nonexistence results for positive solutions are derived in terms of different intervals of parameter. Our approach relies on the Guo–Krasnoselskii fixed point theorem on cones.

Oregano essential oil (OEO), which has antimicrobial properties, may be used for altering the ruminal pH and microbial populations of sheep, as observed by the altered volatile fatty acid patterns. To further elucidate the effects of OEO on ruminal pH and microbial populations of sheep, 3 German merino sheep × local sheep crossbred rams with permanent ruminal fistulas were randomly assigned to a 3 × 3 Latin square design with 12-d periods. The treatments were as follows: control (CON); OEO4: OEO supplied at 4 g•d-1; and OEO7: OEO supplied at 7 g•d-1. Starting on day 11, rumen fluid was collected at 0 h, and at 4, 8, 12, 24 and 48 h after supplying OEO, and then pH values of rumen fluid were immediately measured. The abundance of microbial populations was determined by using qPCR. The ruminal pH values were similar among the sheep from all treatments. The abundance of ruminal fungi was higher for the sheep supplied OEO7 compared with the sheep supplied CON and OEO4, especially at 4 and 12 h. The abundance of ruminal protozoa decreased with supplied OEO, indicating that OEO could inhibit the protozoa. The abundance of the total ruminal bacteria was similar for the sheep from all treatments, but R. flavefaciens, R. albus and F. succinogenes increased in the sheep supplied OEO4 compared with those in the sheep supplied CON, however, the sheep supplied OEO7 had higher abundances of R. flavefaciens than the sheep supplied CON. These results demonstrated that supplying OEO to sheep did not affect the ruminal pH but could shift the rumen microbial population to one with less protozoa. Supplying OEO can preferentially enhance the growth of certain rumen microbial populations, but the shifts were influenced by the supply rate. Therefore, supplying low amount (i.e. 4 g•d-1) of OEO could have positive effects on ruminal microbial populations, whereas supplying elevated doses of OEO could be detrimental to those same ruminal microbial populations.

This article is concerned with a class of singular nonlinear fractional boundary value problems with p-Laplacian operator, which contains Riemann–Liouville fractional derivative and Caputo fractional derivative. The boundary conditions are made up of two kinds of Riemann–Stieltjes integral boundary conditions and nonlocal infinite-point boundary conditions, and different fractional orders are involved in the boundary conditions and the nonlinear term, respectively. Based on the method of reducing the order of fractional derivative, some properties of the corresponding Green’s function, and the fixed point theorem of mixed monotone operator, an interesting result on the iterative sequence of the uniqueness of positive solutions is obtained under the assumption that the nonlinear term may be singular in regard to both the time variable and space variables. And we obtain the dependence of solution upon parameter. Furthermore, two numerical examples are presented to illustrate the application of our main results.

In this article, we study a class of nonlinear fractional differential equations with mixed-type boundary conditions. The fractional derivatives are involved in the nonlinear term and the boundary conditions. By using the properties of the Green function, the fixed point index theory and the Banach contraction mapping principle based on some available operators, we obtain the existence of positive solutions and a unique positive solution of the problem. Finally, two examples are given to demonstrate the validity of our main results.