一类具有推广的Caputo分数阶导数的微分方程的Ulam稳定性  

Ulam’s Stability of Fractional Differential Equations Within a Class of Generalized Caputo Fractional Derivative

作　　者：张玲玲 王森 张孝锋 周先锋[1] ZHANG Lingling;WANG Sen;ZHANG Xiaofeng;ZHOU Xianfeng(School of Mathematics and Science,Anhui University,Hefei 230601,China)

机构地区：[1]安徽大学数学科学学院,安徽合肥230601

出　　处：《应用数学》2024年第3期847-855,共9页Mathematica Applicata

基　　金：the National Natural Science Foundation of China(11471015);the Innovation Project of Anhui University(X202210357008)。

摘　　要：本文研究一类具有推广的Caputo分数阶导数的微分方程,推广的Caputo分数阶导数可由Conformable导数与经典的Caputo导数结合而得或是推广的分数阶算子.我们利用拉普拉斯变换研究了线性方程的Ulam-Hyers稳定性,分别利用Banach不动点定理和Guonwall不等式研究了非线性方程解的存在唯一性和Ulam-Hyers-Rassis稳定性,获得了几个充分条件的定理,并给出一个例子作为所得结果的应用.In this paper,a class of differential equations with a generalized Caputo fractional derivative obtained by combining the conformable derivative with the classical Caputo derivative or derived from generalized fractional operators are considered.We utilize the Laplace transform to investigate the Ulam-Hyers stability of the linear fractional differential equation.Then Banach fixed point theorem and Gronwall inequality are used to study the existence,uniqueness and the Ulam-Hyers-Rassis stability for the solution of the nonlinear differential equation,respectively.Several theorems with sufficient conditions are obtained.An illustrative example is provided as an application of the obtained results.

关 键 词：Ulam稳定性 推广的Caputo分数阶导数 微分方程 

分 类 号：O175.1[理学—数学]