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

Abstract

Abstract 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.

Keywords

• stability
• boundedness
• fractional Duhamel principle
• initial value problem
• time-fractional diffusion equation
• Caputo derivative