Polynomial Expansions for Solutions of Higher-Order Bessel Heat Equation in Quantum Calculus

Ben Hammouda, M.S., and Nemri, Akram. "Polynomial Expansions for Solutions of Higher-Order Bessel Heat Equation in Quantum Calculus." Fractional Calculus and Applied Analysis 10.1 (2007): 39-58. <http://eudml.org/doc/11296>.

@article{BenHammouda2007,
abstract = {Mathematics Subject Class.: 33C10,33D60,26D15,33D05,33D15,33D90In this paper we give the q-analogue of the higher-order Bessel operators studied by I. Dimovski [3],[4], I. Dimovski and V. Kiryakova [5],[6], M. I. Klyuchantsev [17], V. Kiryakova [15], [16], A. Fitouhi, N. H. Mahmoud and S. A. Ould Ahmed Mahmoud [8], and recently by many other authors. 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 [22]. For some value of the vector index, our operator generalizes the q-jα Bessel operator of the second order in [9] and a q-Third operator in [12].},
author = {Ben Hammouda, M.S., Nemri, Akram},
journal = {Fractional Calculus and Applied Analysis},
keywords = {33C10; 33D60; 26D15; 33D05; 33D15; 33D90},
language = {eng},
number = {1},
pages = {39-58},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Polynomial Expansions for Solutions of Higher-Order Bessel Heat Equation in Quantum Calculus},
url = {http://eudml.org/doc/11296},
volume = {10},
year = {2007},
}

TY - JOUR
AU - Ben Hammouda, M.S.
AU - Nemri, Akram
TI - Polynomial Expansions for Solutions of Higher-Order Bessel Heat Equation in Quantum Calculus
JO - Fractional Calculus and Applied Analysis
PY - 2007
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 10
IS - 1
SP - 39
EP - 58
AB - Mathematics Subject Class.: 33C10,33D60,26D15,33D05,33D15,33D90In this paper we give the q-analogue of the higher-order Bessel operators studied by I. Dimovski [3],[4], I. Dimovski and V. Kiryakova [5],[6], M. I. Klyuchantsev [17], V. Kiryakova [15], [16], A. Fitouhi, N. H. Mahmoud and S. A. Ould Ahmed Mahmoud [8], and recently by many other authors. 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 [22]. For some value of the vector index, our operator generalizes the q-jα Bessel operator of the second order in [9] and a q-Third operator in [12].
LA - eng
KW - 33C10; 33D60; 26D15; 33D05; 33D15; 33D90
UR - http://eudml.org/doc/11296
ER -