2007/03/08 by M. S. Ben Hammouda, Hammouda, M. S. Ben, Akram Nemri +1
Mathematics · #26D15 #33C10 #33D05 #33D15 #33D60 #33D90 #Differential Equations and Boundary Problems #FOS: Physical sciences #Mathematical Analysis and Transform Methods #Mathematical Physics (math-ph) #Mathematical functions and polynomials
paper · pdf · doi:10.48550/arxiv.math-ph/0703026
openalex publication_date 2007/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we give the q-analogue of the higher-order Bessel operators studied by M. I. Klyuchantsev [12] and A. Fitouhi, N. H. Mahmoud and S. A. Ould Ahmed Mahmoud [3]. Our objective is twofold. First, using the q-Jackson integral and the q-derivative, we aim at establishing some properties of this function with proofs similar to the classical case. Second our goal is to construct the associated q-Fourier transform and the q-analogue of the theory of the heat polynomials introduced by P. C. Rosenbloom and D. V. Widder [13]. Our operator for some value of the vector index generalize the q-jαBessel operator of the second order in [4] and a q-Third operator in [6].