# q-Heat Operator and q-Poisson’s Operator

• Volume: 9, Issue: 3, page 265-286
• ISSN: 1311-0454

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## Abstract

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2000 Mathematics Subject Classification: 33D15, 33D90, 39A13In this paper we study the q-heat and q-Poisson’s operators associated with the q-operator ∆q (see[5]). We begin by summarizing some statements concerning the q-even translation operator Tx,q, defined by Fitouhi and Bouzeffour in [5]. Then, we establish some basic properties of the q-heat semi-group such as boundedness and positivity. In the second part, we introduce the q-Poisson operator P^t, and address its main properties. We show in particular how these operators can be used to solve the initial and boundary value problems related to the q-heat and q-Laplace equation respectively.

## How to cite

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Mabrouk, Hanène. "q-Heat Operator and q-Poisson’s Operator." Fractional Calculus and Applied Analysis 9.3 (2006): 265-286. <http://eudml.org/doc/11278>.

@article{Mabrouk2006,
abstract = {2000 Mathematics Subject Classification: 33D15, 33D90, 39A13In this paper we study the q-heat and q-Poisson’s operators associated with the q-operator ∆q (see[5]). We begin by summarizing some statements concerning the q-even translation operator Tx,q, defined by Fitouhi and Bouzeffour in [5]. Then, we establish some basic properties of the q-heat semi-group such as boundedness and positivity. In the second part, we introduce the q-Poisson operator P^t, and address its main properties. We show in particular how these operators can be used to solve the initial and boundary value problems related to the q-heat and q-Laplace equation respectively.},
author = {Mabrouk, Hanène},
journal = {Fractional Calculus and Applied Analysis},
keywords = {33D15; 33D90; 39A13},
language = {eng},
number = {3},
pages = {265-286},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {q-Heat Operator and q-Poisson’s Operator},
url = {http://eudml.org/doc/11278},
volume = {9},
year = {2006},
}

TY - JOUR
AU - Mabrouk, Hanène
TI - q-Heat Operator and q-Poisson’s Operator
JO - Fractional Calculus and Applied Analysis
PY - 2006
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 9
IS - 3
SP - 265
EP - 286
AB - 2000 Mathematics Subject Classification: 33D15, 33D90, 39A13In this paper we study the q-heat and q-Poisson’s operators associated with the q-operator ∆q (see[5]). We begin by summarizing some statements concerning the q-even translation operator Tx,q, defined by Fitouhi and Bouzeffour in [5]. Then, we establish some basic properties of the q-heat semi-group such as boundedness and positivity. In the second part, we introduce the q-Poisson operator P^t, and address its main properties. We show in particular how these operators can be used to solve the initial and boundary value problems related to the q-heat and q-Laplace equation respectively.
LA - eng
KW - 33D15; 33D90; 39A13
UR - http://eudml.org/doc/11278
ER -

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