Regularization of Inverse Initial Problem for Conformable Pseudo-Parabolic Equation with Inhomogeneous Term

Abstract

The main goal of the paper is to approximate two types of inverse problems for conformable heat equation (or called parabolic equation with conformable operator); as follows, we considered two cases: the right hand side of equation such that $F\left(x,t\right)$ and $F\left(x,t\right)=\phi \left(t\right)f\left(x\right)$ . Up to now, there are very few surveys working on the results of regularization in ${\mathcal{L}}^p$ spaces. Our paper is the first work to investigate the inverse problem for conformable parabolic equations in such spaces. For the inverse source problem and the backward problem, use the Fourier truncation method to approximate the problem. The error between the regularized solution and the exact solution is obtained in ${\mathcal{L}}^p$ under some suitable assumptions on the Cauchy data.