# The General Fractional Integrals and Derivatives on a Finite Interval

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. The General Fractional Integrals on a Finite Interval

**Definition**

**1.**

**Definition**

**2.**

**Proposition**

**1.**

**Proof.**

**Proposition**

**2.**

**Proof.**

**Proposition**

**3.**

**Proof.**

## 3. The General Fractional Derivatives on a Finite Interval

**Definition**

**3.**

**Proposition**

**4.**

**Proof.**

**Proposition**

**5.**

**Proof.**

**Theorem**

**1.**

**Proof.**

**Remark**

**1.**

**Theorem**

**2.**

**Proof.**

## 4. Conclusions and Directions for Further Research

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**MDPI and ACS Style**

Al-Refai, M.; Luchko, Y.
The General Fractional Integrals and Derivatives on a Finite Interval. *Mathematics* **2023**, *11*, 1031.
https://doi.org/10.3390/math11041031

**AMA Style**

Al-Refai M, Luchko Y.
The General Fractional Integrals and Derivatives on a Finite Interval. *Mathematics*. 2023; 11(4):1031.
https://doi.org/10.3390/math11041031

**Chicago/Turabian Style**

Al-Refai, Mohammed, and Yuri Luchko.
2023. "The General Fractional Integrals and Derivatives on a Finite Interval" *Mathematics* 11, no. 4: 1031.
https://doi.org/10.3390/math11041031