# Particular Solutions of the Confluent Hypergeometric Differential Equation by Using the Nabla Fractional Calculus Operator

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Preliminaries

**Definition 2.1.**[6] The rising factorial power is given by:

**Definition 2.2.**[6] The $\alpha -\chi h$ order fractional sum of $\varpi $ is given by:

**Theorem 2.1.**

**Lemma 2.1.**

**Lemma 2.2.**

## 3. Main Results

**Theorem 3.1.**

**Proof.**

**Theorem 3.2.**

**Proof.**

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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Yilmazer, R.; Inc, M.; Tchier, F.; Baleanu, D.
Particular Solutions of the Confluent Hypergeometric Differential Equation by Using the Nabla Fractional Calculus Operator. *Entropy* **2016**, *18*, 49.
https://doi.org/10.3390/e18020049

**AMA Style**

Yilmazer R, Inc M, Tchier F, Baleanu D.
Particular Solutions of the Confluent Hypergeometric Differential Equation by Using the Nabla Fractional Calculus Operator. *Entropy*. 2016; 18(2):49.
https://doi.org/10.3390/e18020049

**Chicago/Turabian Style**

Yilmazer, Resat, Mustafa Inc, Fairouz Tchier, and Dumitru Baleanu.
2016. "Particular Solutions of the Confluent Hypergeometric Differential Equation by Using the Nabla Fractional Calculus Operator" *Entropy* 18, no. 2: 49.
https://doi.org/10.3390/e18020049