TY - JOUR
T1 - The Fractional Laguerre Equation
T2 - Series Solutions and Fractional Laguerre Functions
AU - Shat, Rasha
AU - Alrefai, Safa
AU - Alhamayda, Islam
AU - Sarhan, Alaa
AU - Al-Refai, Mohammed
N1 - Funding Information:
The authors gratefully acknowledge the support of the United Arab Emirates University under the SURE+ grant no. 31S291−26−2− SURE+2017.
Publisher Copyright:
© Copyright © 2019 Shat, Alrefai, Alhamayda, Sarhan and Al-Refai.
PY - 2019/2/20
Y1 - 2019/2/20
N2 - In this paper, we propose a fractional generalization of the well-known Laguerre differential equation. We replace the integer derivative by the conformable derivative of order 0 < α < 1. We then apply the Frobenius method with the fractional power series expansion to obtain two linearly independent solutions of the problem. For certain eigenvalues, the infinite series solution truncate to obtain the singular and non-singular fractional Laguerre functions. We obtain the fractional Laguerre functions in closed forms, and establish their orthogonality result. The applicability of the new fractional Laguerre functions is illustrated.
AB - In this paper, we propose a fractional generalization of the well-known Laguerre differential equation. We replace the integer derivative by the conformable derivative of order 0 < α < 1. We then apply the Frobenius method with the fractional power series expansion to obtain two linearly independent solutions of the problem. For certain eigenvalues, the infinite series solution truncate to obtain the singular and non-singular fractional Laguerre functions. We obtain the fractional Laguerre functions in closed forms, and establish their orthogonality result. The applicability of the new fractional Laguerre functions is illustrated.
KW - Frobenius method
KW - Laguerre equation
KW - conformable fractional derivative
KW - fractional differential equations
KW - series solution
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U2 - 10.3389/fams.2019.00011
DO - 10.3389/fams.2019.00011
M3 - Article
AN - SCOPUS:85074584717
SN - 2297-4687
VL - 5
JO - Frontiers in Applied Mathematics and Statistics
JF - Frontiers in Applied Mathematics and Statistics
M1 - 11
ER -