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Entropy 2016, 18(2), 49; doi:10.3390/e18020049

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

1
Department of Mathematics, Science Faculty, Fırat University, Elazığ 23119, Turkey
2
Department of Mathematics, King Saud University, P.O. Box 22452, Riyadh 11495, Saudi Arabia
3
Department of Mathematics and Computer Science, Çankaya University, Ankara 06530, Turkey
4
Institute of Space Sciences, P.O. Box MG-23, Magurele-Bucharest RO-76911, Romania
*
Author to whom correspondence should be addressed.
Academic Editors: J. A. Tenreiro Machado, António M. Lopes and Kevin H. Knuth
Received: 13 November 2015 / Revised: 25 January 2016 / Accepted: 27 January 2016 / Published: 5 February 2016
(This article belongs to the Special Issue Complex and Fractional Dynamics)
View Full-Text   |   Download PDF [204 KB, uploaded 5 February 2016]

Abstract

In this work; we present a method for solving the second-order linear ordinary differential equation of hypergeometric type. The solutions of this equation are given by the confluent hypergeometric functions (CHFs). Unlike previous studies, we obtain some different new solutions of the equation without using the CHFs. Therefore, we obtain new discrete fractional solutions of the homogeneous and non-homogeneous confluent hypergeometric differential equation (CHE) by using a discrete fractional Nabla calculus operator. Thus, we obtain four different new discrete complex fractional solutions for these equations. View Full-Text
Keywords: discrete fractional calculus; confluent hypergeometric equation; Nabla operator discrete fractional calculus; confluent hypergeometric equation; Nabla operator
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS 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, 49.

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