A solely time-dependent source reconstruction in a multiterm time-fractional order diffusion equation with non-smooth solutions

An inverse source problem for non-smooth multiterm time Caputo fractional diffusion with order designed as β0 < β1 ⋯ βM 1 is the case of study in a bounded Lipschitz domain $\mathbb {R}^{d}$ . The missing solely time-dependent function reconstructed from an additional integral measurement. existence, uniqueness and regularity weak solution investigated. We design numerical algorithm based on Rothe’s method over graded meshes, derive priori estimates prove convergence iterates towards exact solution. essential feature subdiffusion that possibly lacks smoothness near initial time, although it would be smooth away t = 0. In this contribution, we will establish extension Grönwall’s inequalities operators. This crucial showing existence unique to problem. theoretical obtained results are supported by some experiments.