On the Laguerre fractional integro-differentiation

2020/03/11 by Semyon Yakubovich, Yakubovich, Semyon
Mathematics · #33C05 #44A15 #45E10 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:33C05 #msc:44A15 #msc:45E10

paper · pdf · doi:10.48550/arxiv.2003.05335

arxiv created 2020/07/10 · arxiv updated 2020/07/13

Abstract

A fractional power interpretation of the Laguerre derivative (DxD)^α, D≡ d\over dx is discussed. The corresponding fractional integrals are introduced. Mapping and semigroup properties, integral representations and Mellin transform analysis are presented. A relationship with the Riemann-Liouville fractional integrals is demonstrated. Finally, a second kind integral equation of the Volterra-type, involving the Laguerre fractional integral is solved in terms of the double hypergeometric type series as the resolvent kernel.

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