On the fractional Bessel operator
Fethi Bouzeffour, Mübariz Garayev
Abstract
In this paper, we investigate the fractional power (−Δν)γ/2, 0<γ<2, of the Bessel operator in the form Δν:=d2dx2+2ν+1xddx,ν>−1/2. Our method uses a canonical representation for generalized Laplacian related to the structures of the Bessel–Kingman hypergroup. As a direct application, we solve the space-fractional diffusion equation.
Topics & Concepts
Bessel functionMathematicsOperator (biology)Laplace operatorRepresentation (politics)Bessel processCylindrical harmonicsBessel polynomialsMathematical analysisFractional calculusSpace (punctuation)Pure mathematicsOrthogonal polynomialsGegenbauer polynomialsPolitical scienceBiochemistryGenePhilosophyTranscription factorLawLinguisticsChemistryRepressorPoliticsClassical orthogonal polynomialsAdvanced Harmonic Analysis ResearchDifferential Equations and Boundary ProblemsNonlinear Differential Equations Analysis