分数和泛函微分方程是数学的两个热门话题,他们有多个应用程序在不同分支的科学和工程。这两种类型的微分方程的组合会导致一些有趣的结果从理论和应用的观点。

这个特殊问题的目的是为了讨论一些新的算法和方法用于调查分数和泛函微分方程。下面我们给出一个简短的调查内容的这个特殊的问题。

存在正解的理论与偏差变元二阶奇异微分方程及其参数依赖被报道。黎兹空间并行快速解决方案部分反应扩散方程进行了研究。正解的状态与分数阶微分运营商依赖的边值问题被发现。步长限制非线性中立型时滞微分方程的稳定性能和格林函数和二阶奇异边值问题正解的积分边界条件和延迟参数研究。分数阶系统复杂的动力学和同步变量,Riemann-Liouville部分边值问题解的存在,和概周期解的存在性脉冲中立型泛函微分方程是其他主题的特殊问题。分数微分方程与部分冲动和nonseparated边界条件和全球长期衰变Fourier-Besov分数n - s方程的适定性问题空间被报道。参数估计的随机微分方程由混合分数布朗运动驱动,解决方案的非线性Erdelyi-Kober积分方程,基于RBF神经网络和小说的内核是其他学科的特殊问题。数值算法的三阶偏微分方程三点边值问题,建模的非线性波动范围内分数微积分,广义Kudryashov time-fractional微分方程的方法。一个新颖的方法来处理偏微分方程和混合衍生品,分数微分方程的变分迭代变换方法与当地分数导数,一个有效的搭配方法,一类边值问题出现在数学物理和几何,和为进化伪微分方程柯西问题p进领域进行了分析。新超球面小波部分黎卡提微分光谱解微分方程,非线性Gronwall-Bellman-Gamidov积分不等式及其弱奇异类似物应用程序,一个新的勒让德搭配方法求解atwo-dimensional部分扩散方程,计算光谱与高斯乘数狄拉克不连续系统的参数,并分析研究分数阶多个混沌FitzHugh-Nagumo神经元模型使用多步广义微分变换方法是有趣的报道主题。 The small time asymptotics of SPDEs with reflection, the convergence of variational iteration method for solving singular partial differential equations with fractional order, the fourth-order compact difference scheme for the Riemann-Liouville and Riesz derivatives, the existence of solutions for fractional boundary value problem with nonlinear derivative dependence, and regularized fractional power parameters for image denoising based on convex solution of fractional heat equation were distinct topics of our special issue. Solving the Fokker-Planck equations on Cantor sets using local fractional decomposition method was also reported and an efficient series solution for fractional differential equations was analyzed. Two hybrid methods for solving two-dimensional linear time-fractional partial differential equations and the application of local fractional series expansion method to solve Klein-Gordon equations on Cantor sets are subjects investigated by the authors of our special issue. A pseudo-spectral algorithm for solving multipantograph delay systems on a semi-infinite interval using Legendre rational functions was developed and a modified groundwater flow model using the space time Riemann-Liouville fractional derivatives approximation was reported.

Dumitru Baleanu
阿里·h·Bhrawy
罗伯特·范·Gorder