# On nonlinear Sobolev equations with terminal observations in \(L^p\) spaces

## Keywords:

Conformable derivative, Fourier truncation method, Regularization## Abstract

In this paper, we investigate the backward problem for the heat equation equipped with the time fractional conformable derivative. This problem is a generalization of the classical heat equation. We consider the problem with a nonlinear source function in a bounded domain. This problem is shown to be ill-posed, so we regularize the solution by the Fourier truncated method and we estimate the error term in the \(L^p(\mathcal{D})\) space. An example to illustrate the theory is given in the final section.

### Additional Files

## Published

09-05-2023

## How to Cite

*Letters on Applied and Pure Mathematics*,

*1*(1), 32–45. Retrieved from https://lapmjournal.com/index.php/lapm/article/view/lapm.2023v1n1-4

## Issue

## Section

Research Article

## License

Copyright (c) 2023 Letters on Applied and Pure Mathematics

This work is licensed under a Creative Commons Attribution 4.0 International License.