Inverse source problem for multi-term time-fractional diffusion equation with nonlocal boundary conditions

Abstract

In this paper, we consider an inverse source problem with nonlocal boundary conditions for the heat equation involving multi-term time-fractional derivatives. We determine a source term independent of the space variable, and the temperature distribution from the energy measurement. We reduce the solution of the inverse problem to finding solutions to two problems. The well-posedness of each problem is shown using the generalized Fourier method.

Keywords

• inverse source problem
• fractional diffusion equation
• nonlocal boundary condition
• multinomial mittag-lefler function
• fourier series