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1.
In this paper, the problem of the uniform stability for a class of fuzzy fractional-order genetic regulatory networks with random discrete delays, distributed delays, and parameter uncertainties is studied. Although there is a portion of literature on using fixed point theorems to study the stability of fractional neural networks, most of them required the fractional order to be in 1 2 , 1 . However, the case of the fractional-order belonging to ( 0 , 1 2 ) has not been discussed. To solve it, this work proposes a novel idea of using fixed point theory to study the stability of fuzzy (0,1) order neural networks, the problem of the uniqueness of the solution of the considered genetic regulatory networks is resolved, and a novel sufficient condition to guarantee the uniform stability of above genetic regulatory networks is also derived. Eventually, an example is given to demonstrate that the obtained result is effective.  相似文献   
2.

The purpose of this investigation is to theoretically shed some light on the effect of the unsteady electroosmotic flow (EOF) of an incompressible fractional second-grade fluid with low-dense mixtures of two spherical nanoparticles, copper, and titanium. The flow of the hybrid nanofluid takes place through a vertical micro-channel. A fractional Cattaneo model with heat conduction is considered. For the DC-operated micropump, the Lorentz force is responsible for the pressure difference through the microchannel. The Debye-Hükel approximation is utilized to linearize the charge density. The semi-analytical solutions for the velocity and heat equations are obtained with the Laplace and finite Fourier sine transforms and their numerical inverses. In addition to the analytical procedures, a numerical algorithm based on the finite difference method is introduced for the given domain. A comparison between the two solutions is presented. The variations of the velocity heat transfer against the enhancements in the pertinent parameters are thoroughly investigated graphically. It is noticed that the fractional-order parameter provides a crucial memory effect on the fluid and temperature fields. The present work has theoretical implications for biofluid-based microfluidic transport systems.

  相似文献   
3.
In this paper, we consider the existence and uniqueness of solutions to time-varying delays stochastic fractional differential equations (SFDEs) with non-Lipschitz coefficients. By using fractional calculus and stochastic analysis, we can obtain the existence result of solutions for stochastic fractional differential equations.  相似文献   
4.
The pivotal aim of the present work is to find the numerical solution for fractional Benney–Lin equation by using two efficient methods, called q ‐homotopy analysis transform method and fractional natural decomposition method. The considered equation exemplifies the long waves on the liquid films. Projected methods are distinct with solution procedure and they are modified with different transform algorithms. To illustrate the reliability and applicability of the considered solution procedures we consider eight special cases with different initial conditions. The fractional operator is considered in Caputo sense. The achieved results are drowned through two and three‐dimensional plots for different Brownian motions and classical order. The numerical simulations are presented to ensure the efficiency of considered techniques. The behavior of the obtained results for distinct fractional order is captured in the present framework. The outcomes of the present investigation show that, the considered schemes are efficient and powerful to solve nonlinear differential equations arise in science and technology.  相似文献   
5.
In this paper, we study the Holder regularity of weak solutions to the Dirichlet problem associated with the regional fractional Laplacian (-△)αΩ on a bounded open set Ω ■R(N ≥ 2) with C(1,1) boundary ■Ω. We prove that when f ∈ Lp(Ω), and g ∈ C(Ω), the following problem (-△)αΩu = f in Ω, u = g on ■Ω, admits a unique weak solution u ∈ W(α,2)(Ω) ∩ C(Ω),where p >N/2-2α and 1/2< α < 1. To solve this problem, we consider it into two special cases, i.e.,g ≡ 0 on ■Ω and f ≡ 0 in Ω. Finally, taking into account the preceding two cases, the general conclusion is drawn.  相似文献   
6.
In this article, a way to employ the diffusion approximation to model interplay between TCP and UDP flows is presented. In order to control traffic congestion, an environment of IP routers applying AQM (Active Queue Management) algorithms has been introduced. Furthermore, the impact of the fractional controller PIγ and its parameters on the transport protocols is investigated. The controller has been elaborated in accordance with the control theory. The TCP and UDP flows are transmitted simultaneously and are mutually independent. Only the TCP is controlled by the AQM algorithm. Our diffusion model allows a single TCP or UDP flow to start or end at any time, which distinguishes it from those previously described in the literature.  相似文献   
7.
In this paper, first, we prove the weighted Hermite–Hadamard–Mercer inequalities for convex functions, after we establish some new weighted inequalities connected with the right‐sides of weighted Hermite–Hadamard–Mercer type inequalities for differentiable functions whose derivatives in absolute value at certain powers are convex. The results presented here would provide extensions of those given in earlier works.  相似文献   
8.
当初值不光滑时,时间分数阶齐次扩散方程数值方法的精度会下降.为了得到高阶时间收敛格式,提出加权移位的Grünwald-Letnikov的修正格式,运用Lubich的修正方法,得到非光滑时间分数阶齐次扩散方程的收敛阶仍为O(k2).最后,通过数值算例验证了数值计算结果与理论计算结果一致.  相似文献   
9.
Although most of the early research studies on fractional-order systems were based on the Caputo or Riemann–Liouville fractional-order derivatives, it has recently been proven that these methods have some drawbacks. For instance, kernels of these methods have a singularity that occurs at the endpoint of an interval of definition. Thus, to overcome this issue, several new definitions of fractional derivatives have been introduced. The Caputo–Fabrizio fractional order is one of these nonsingular definitions. This paper is concerned with the analyses and design of an optimal control strategy for a Caputo–Fabrizio fractional-order model of the HIV/AIDS epidemic. The Caputo–Fabrizio fractional-order model of HIV/AIDS is considered to prevent the singularity problem, which is a real concern in the modeling of real-world systems and phenomena. Firstly, in order to find out how the population of each compartment can be controlled, sensitivity analyses were conducted. Based on the sensitivity analyses, the most effective agents in disease transmission and prevalence were selected as control inputs. In this way, a modified Caputo–Fabrizio fractional-order model of the HIV/AIDS epidemic is proposed. By changing the contact rate of susceptible and infectious people, the atraumatic restorative treatment rate of the treated compartment individuals, and the sexual habits of susceptible people, optimal control was designed. Lastly, simulation results that demonstrate the appropriate performance of the Caputo–Fabrizio fractional-order model and proposed control scheme are illustrated.  相似文献   
10.
目前浮选提高重晶石品位的方法通常采用新型浮选药剂从低品位重晶石矿中进行分选,采用微波加热预处理矿物可提高浮选回收率,但微波对浮选药剂与矿物的作用机理还不清楚。微波加热技术近年来用于矿物加工、冶金与材料制备等领域,具有反应速度快、产品指标高等优点。以油酸钠为捕收剂,对微波预处理后的重晶石纯矿物进行浮选,并对不同微波作用时间下的重晶石浮选样品进行红外光谱检测,通过红外拟合平滑光谱和二阶导数光谱计算分析,研究微波对重晶石浮选的影响机理。浮选试验结果表明,未经微波预处理的重晶石,在油酸钠用量为55 mg·L-1、pH值为8.0的条件下,浮选指标最佳,回收率为91.41%;而对比之下,经微波作用后的重晶石进行浮选,随着微波处理时间的增加浮选指标逐渐提高,且在微波作用60s时的回收率最高,达95.27%。基于浮选试验的红外光谱分析表明,重晶石未经微波预处理进行浮选,与油酸钠作用,在波数为3 004 cm-1处-CH2-的对称伸缩振动峰、2 953 cm-1处-CH3的反对称伸缩振动峰、1 119和1 077 cm-1处SO2-4的非对称伸缩振动峰均发生了红移,说明油酸钠在重晶石表面发生化学吸附;而经微波预处理后的重晶石浮选时,在波数为2 853 cm-1处-CH2-对称伸缩振动峰、2 923 cm-1处-CH2-反对称伸缩振动峰、2 958 cm-1处-CH3反对称伸缩振动峰、1 181,1 122和1 086 cm-1处SO2-4非对称伸缩振动峰、982 cm-1处SO2-4对称伸缩振动峰、635和610 cm-1处SO2-4弯曲振动峰,其峰位并未发生红移,但峰强随着微波作用时间的增加明显加强,且微波作用60 s时其峰强增加最明显;对微波处理后的红外光谱进行拟合平滑光谱和二阶导数光谱计算发现,在波数为2 958,2 923,2 853,1 181,1 122,1 086,982,635和610 cm-1处峰面积均有不同程度的增加,且在微波作用60s时峰面积分别增加了1.84%,259.12%,761.15%,235.72%,145.61%,198.50%,641.16%,549.67%和744.97%,表明微波预处理并未诱发重晶石表面发生化学反应,但强化了捕收剂油酸钠与重晶石矿之间的化学吸附,使其与重晶石表面的化学吸附更加致密,吸附量增加,因此重晶石回收率增加,浮选指标提高。  相似文献   
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