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

Fractional Calculus and Applied Analysis (2006)

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

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topMabrouk, 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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