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

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 < α < 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. [ABSTRACT FROM AUTHOR]