Fractional Frobenius Series Solutions of Confluent α-Hypergeometric Differential Equation

Ma’mon Abu Hammad; Iqbal H. Jebril; Iqbal M. Batiha; Amer Mansour Dababneh

doi:10.18576/pfda/080209

Fractional Frobenius Series Solutions of Confluent α-Hypergeometric Differential Equation

Ma’mon Abu Hammad
, Iqbal H. Jebril
, Iqbal M. Batiha
, Amer Mansour Dababneh

Nonlinear Dynamic Research Centre (NDRC)

Al-Zaytoonah University of Jordan
Irbid National University

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

In this work, the so-called conformable fractional derivative definition is employed to obtain the fractional Frobenius series solutions around the regular α-singular point x = 0 for the confluent α-hypergeometric differential equation. Of course, such solutions for this equation in its classical case are just confluent hypergeometric functions. The proposed method is straightforward to be applied as an algorithm.

Original language	English
Pages (from-to)	297-304
Number of pages	8
Journal	Progress in Fractional Differentiation and Applications
Volume	8
Issue number	2
DOIs	https://doi.org/10.18576/pfda/080209
State	Published - Apr 2022

Keywords

Confluent hypergeometric differential equations
Confluent hypergeometric function
Conformable fractional derivative definition
Fractional frobenius series
Regular a-singular point

Access to Document

10.18576/pfda/080209

Cite this

@article{d46cfe5638cf4773b85a64675649754d,

title = "Fractional Frobenius Series Solutions of Confluent α-Hypergeometric Differential Equation",

abstract = "In this work, the so-called conformable fractional derivative definition is employed to obtain the fractional Frobenius series solutions around the regular α-singular point x = 0 for the confluent α-hypergeometric differential equation. Of course, such solutions for this equation in its classical case are just confluent hypergeometric functions. The proposed method is straightforward to be applied as an algorithm.",

keywords = "Confluent hypergeometric differential equations, Confluent hypergeometric function, Conformable fractional derivative definition, Fractional frobenius series, Regular a-singular point",

author = "Hammad, \{Ma{\textquoteright}mon Abu\} and Jebril, \{Iqbal H.\} and Batiha, \{Iqbal M.\} and Dababneh, \{Amer Mansour\}",

note = "Publisher Copyright: {\textcopyright} 2022. NSP Natural Sciences Publishing Cor.",

year = "2022",

month = apr,

doi = "10.18576/pfda/080209",

language = "English",

volume = "8",

pages = "297--304",

journal = "Progress in Fractional Differentiation and Applications",

issn = "2356-9336",

publisher = "Natural Sciences Publishing",

number = "2",

}

TY - JOUR

T1 - Fractional Frobenius Series Solutions of Confluent α-Hypergeometric Differential Equation

AU - Hammad, Ma’mon Abu

AU - Jebril, Iqbal H.

AU - Batiha, Iqbal M.

AU - Dababneh, Amer Mansour

PY - 2022/4

Y1 - 2022/4

N2 - In this work, the so-called conformable fractional derivative definition is employed to obtain the fractional Frobenius series solutions around the regular α-singular point x = 0 for the confluent α-hypergeometric differential equation. Of course, such solutions for this equation in its classical case are just confluent hypergeometric functions. The proposed method is straightforward to be applied as an algorithm.

AB - In this work, the so-called conformable fractional derivative definition is employed to obtain the fractional Frobenius series solutions around the regular α-singular point x = 0 for the confluent α-hypergeometric differential equation. Of course, such solutions for this equation in its classical case are just confluent hypergeometric functions. The proposed method is straightforward to be applied as an algorithm.

KW - Confluent hypergeometric differential equations

KW - Confluent hypergeometric function

KW - Conformable fractional derivative definition

KW - Fractional frobenius series

KW - Regular a-singular point

UR - https://www.scopus.com/pages/publications/85129693930

U2 - 10.18576/pfda/080209

DO - 10.18576/pfda/080209

M3 - Article

AN - SCOPUS:85129693930

SN - 2356-9336

VL - 8

SP - 297

EP - 304

JO - Progress in Fractional Differentiation and Applications

JF - Progress in Fractional Differentiation and Applications

IS - 2

ER -

Fractional Frobenius Series Solutions of Confluent α-Hypergeometric Differential Equation

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this