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

Ben Hammouda, M.S.; Nemri, Akram

Fractional Calculus and Applied Analysis (2007)

- Volume: 10, Issue: 1, page 39-58
- ISSN: 1311-0454

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topBen 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 -

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