关于分数阶偏泛函微分方程基本理论的研究

项目名称： 关于分数阶偏泛函微分方程基本理论的研究

项目编号： No.11471015

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 周先锋

作者单位： 安徽大学

项目金额： 75万元

中文摘要： 分数阶微分方程在建模一些具有记忆过程、遗传性质以及异质材料时比整数阶微分方程模型更具优势。粘弹性系统、电解质极化系统、生物系统中的电导、分形动力学、混沌的同步等都可以用分数阶微分系统来描述其本质规律。分数阶常微分方程、分数阶偏微分方程、分数阶泛函微分方程理论已经得到了很好的发展，广泛而深入地研究分数阶偏泛函微分方程理论是必然的趋势。然而，目前对分数阶偏泛函微分方程理论的研究刚刚起步。本项目拟研究线性、非线性、常系数、变系数等分数阶偏泛函微分方程初值问题和边值问题解的存在性、唯一性、稳定性等基本理论和Banach空间中的相关问题。本项目的研究结果将丰富和发展偏微分方程理论、泛函微分方程理论和分数阶微分方程理论。

中文关键词： 分数阶导数；偏泛函的；微分方程

英文摘要： Fractional differential equations possess more advantages than integer-order differential equations in modelling some memory processes, hereditary properties and heterogenerous materials.The essential laws of viscoelastic systems, dielectric polarization systems, electric conduction in biological systems,fractal dynamics and synchronization of chaos,etc,can be described properly by fractional differential systems.The theory of fractional ordinary differential equations, fractional partial differential equations and fractional functional differential equations have gained good developments.Studying of fractional partial functional differential equations extensively and deeply is inevitable tendency.At present, however,investigation of the theory of fractional partial functional differential equations has just started.This project aims to deal with the fundamental theory such as the existence,the uniqueness and the continuous dependence,etc,of fractional partial functional differential equations with initial problems,boundary value problems and the related problems in Banach space.The results of investigation of this project will enrich and develop the theory of parital differential equations,functional differential equations and fractional differential equations.

英文关键词： Fractional derivative;partial functional;differential equations