# The fractional in time Schr\"{o}dinger equation with a Hartree perturbation

## TL;DR

This paper investigates the mathematical properties of a nonlinear fractional Schrödinger equation with a fractional time derivative and Hartree-type nonlinear term, focusing on existence, uniqueness, and regularity of solutions.

## Contribution

It establishes foundational results on the existence, uniqueness, and regularity for a fractional Schrödinger equation with a Hartree perturbation, extending classical analysis to fractional derivatives.

## Key findings

- Proves existence of solutions under certain conditions.
- Demonstrates uniqueness of solutions.
- Analyzes regularity properties of solutions.

## Abstract

The aim of this work is to show existence, uniqueness and regularity properties of nonlinear fractional Schr\"{o}dinger equation with fractional time derivative of order $\alpha\in (0,1)$ and with a Hartree-type nonlinear term.