An inverse source problem of a semilinear time-fractional reaction–diffusion equation

Abstract

In this paper, we investigate an inverse problem of determining the time-dependent source coefficient in a semilinear reaction–diffusion equation involving the Caputo fractional time derivative of order $0<\alpha <1$ in the case of nonlocal boundary and integral overdetermination conditions. We prove the existence and uniqueness of the classical solution by Fourier analysis and the iteration method. Moreover, we show the continuous dependence of this solution upon the additional data of the inverse problem.

Keywords:

• Inverse source problem
• reaction–diffusion equation
• time-fractional derivative
• boundary conditions
• iteration method

2020 Mathematics Subject Classifications:

• 35K57
• 26A33
• 35R30

Acknowledgments

The authors thank the anonymous reviewer for his/her comments which considerably improved the revision of this article.

Disclosure statement

No potential conflict of interest was reported by the author(s).