# Well-posedness and numerical approximation of tempered fractional terminal value problems

## TL;DR

This paper investigates the well-posedness and develops numerical methods for solving tempered fractional terminal value problems of the Caputo type, providing theoretical analysis and numerical evidence of effectiveness.

## Contribution

It introduces three numerical schemes for tempered fractional terminal value problems and analyzes their efficiency and theoretical properties.

## Key findings

- Existence and uniqueness of solutions established
- Numerical schemes demonstrate high accuracy and efficiency
- Theoretical results confirmed by numerical examples

## Abstract

For a class of tempered fractional terminal value problems of the Caputo type, we study the existence and uniqueness of the solution, analyse the continuous dependence on the given data and using a shooting method, we present and discuss three numerical schemes for the numerical approximation of such problems. Some numerical examples are considered in order to illustrate the theoretical results and evidence the efficiency of the numerical methods.