Stability and boundedness of solutions of the initial value problem for a class of time-fractional diffusion equations

Advances in Difference Equations

Jun Wang¹  Yanhua Wen¹  Xian-Feng Zhou¹ 

[1] School of Mathematical Sciences, Anhui University, Hefei, China

关键词: stability;    boundedness;    fractional Duhamel principle;    initial value problem;    time-fractional diffusion equation;    Caputo derivative;   

DOI  :  10.1186/s13662-017-1271-6

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

The aim of this paper is to study the stability and boundedness of solutions of the initial value problem for a class of time-fractional diffusion equations. We first establish a fractional Duhamel principle for the nonhomogeneous time-fractional diffusion equation. Then based on it and the superposition principle, the solution of the above initial value problem is represented. Finally, we obtain the stability and boundedness of the solution and present an illustrative example.

【 授权许可】

CC BY