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1.
本文利用含参变量广义积分计算中常用的求导和变量替换等技巧等给出了傅里叶变换中一个重要的含参变量广义积分的计算方法.  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.
运用边界积分法研究了四边简支、两对边固定另两对边简支、四边固定三种复杂边界条件下厚矩形板的受迫振动问题,求解过程清晰,从而给出了受迫振动控制方程和挠曲面方程。通过在Matlab平台上进行数值计算,得出了图表形式的计算结果,并与有限元模拟值进行对照。研究表明,边界积分法用于求解厚矩形板的受迫振动问题的准确性,本文推导的控制方程和挠曲面方程的正确性,进而对工程实际中的各种相关问题具有一定的现实意义,也为求解此类问题提供了一种新途径,可以直接运用到工程实际中。  相似文献   
4.
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   
5.
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   
6.
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   
7.
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   
8.
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   
9.
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   
10.
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   
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