On the fractional Legendre equation and fractional Legendre functions

Mohammed Al-Refai, Muhammed Syam, Qasem Al-Mdallal

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


In this paper we propose a fractional generalization of the well-known Legendre equation. We obtain a solution in the form of absolutely convergent power series with radius of convergence 1. We then truncate the power series to obtain the even and odd fractional Legendre functions in closed forms. These functions converge to the Legendre polynomials as the fractional derivative approaches 1, and new explicit formulas of the even and odd Legendre polynomials have been derived.

Original languageEnglish
Pages (from-to)93-102
Number of pages10
JournalProgress in Fractional Differentiation and Applications
Issue number2
Publication statusPublished - Apr 1 2017


  • Caputo fractional derivative
  • Fractional differential equations
  • Legendre equation

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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