The Fractional Laguerre Equation: Series Solutions and Fractional Laguerre Functions

Rasha Shat, Safa Alrefai, Islam Alhamayda, Alaa Sarhan, Mohammed Al-Refai

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


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.

Original languageEnglish
Article number11
JournalFrontiers in Applied Mathematics and Statistics
Publication statusPublished - Feb 20 2019
Externally publishedYes


  • Frobenius method
  • Laguerre equation
  • conformable fractional derivative
  • fractional differential equations
  • series solution

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistics and Probability


Dive into the research topics of 'The Fractional Laguerre Equation: Series Solutions and Fractional Laguerre Functions'. Together they form a unique fingerprint.

Cite this