Identifying inverse source for diffusion equation with conformable time derivative by Fractional Tikhonov method

Abstract

In this paper, we study inverse source for diffusion equation with conformable derivative: $CoD_{t}^{(\gamma)}u - \Delta u = \Phi(t) \mathcal{F}(x)$, where $0<\gamma<1,~ (x,t) \in \Omega \times (0,T)$. We survey the following issues: The error estimate between the sought solution and the regularized solution under a priori parameter choice rule; The error estimate between the sought solution and the regularized solution under a posteriori \\ parameter choice rule; Regularization and ${\mathscr L}_{p}$ estimate by Truncation method.