On the source problem for the diffusion equations with conformable derivative - Van Anh Nghiem Thi; Anh Tuan Vu; Dinh Long Le; Vuong Nguyen Doan (Modern Mathematical Methods)
In this article, we are interested in the problem of finding the source function of the diffusions equations \(\partial_{t}^α - Δ u = f(x)\) (where \(f\) as the unknown source function and \(α\in (0,1)\)). Furthermore, the fractional derivative \(α\) of \(u\) is defined by the Conformable time derivative. This is an ill-posed problem. So, we use the Reguralized Tikhonov method to construct a regularization solution, and the estimation of convergence is also discussed.