陈攀峰许学成一类分数阶微分方程解的存在性.doc

摘 要
分数阶微分方程近年来越来越多的用于描述光学和热学系统、控制技术、机器人等应用领域中的问题，特别是从实际问题中抽象出来的一类分数阶微分方程解的存在性对解决实际应用问题提供了很大的帮助。本文主要论述了分数阶微分方程的发展，介绍了将一般形式的分数阶微分方程转化为等价积分方程法证明其解的存在性,，介绍了微分方程在粘弹性材料模型、控制模型、变分原理以及扩散波动方程中的应用.
关键词：分数阶微分方程; 不动点定理; Banach压缩映射原理
ABSTRACT
Recent years, the fractional differential equations are increasingly used to describe optical and thermal system, controlling technique， robots， and other application fields. Especially, the existence of solutions of fractional differential equations which is abstracted from the practice gives a great help to solve the problems. This paper introduces the development of the fractional differential equations。 Then it discusses the proof of the existence of solutions by transforming fractional differential equations into equivalent integral equations， and it also proves the existence of solutions of nonlinear fractional diff