Inverse initial value problem for space-time fractional diffusion equations

Abstract This paper addresses an inverse problem associated with a space-time fractional diffusion equation, specifically focusing on the task of recovering the initial condition using additional final data. Through the application of the eigenfunction expansion method, we establish the well-posedness of this inverse problem in the Hadamard sense. Our analysis confirms the existence of a unique solution for the initial inverse problem and highlights the possibility of recovering the unknown term with Lipschitz stability. To further illustrate the effectiveness of our approach, we present several numerical examples that showcase its accuracy and efficiency. 2020 Mathematics Subject Classification: 34M50, 65M32, 26A33, 34A45.