Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/1283

 Title: q-Heat Operator and q-Poisson’s Operator Authors: Mabrouk, Hanène Keywords: q-Special Functionsq-Operatorsq-Transformsq-Heat Equation33D1533D9039A13 Issue Date: 2006 Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences Citation: Fractional Calculus and Applied Analysis, Vol. 9, No 3, (2006), 265p-286p Abstract: In 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. Description: 2000 Mathematics Subject Classification: 33D15, 33D90, 39A13 URI: http://hdl.handle.net/10525/1283 ISSN: 1311-0454 Appears in Collections: 2006

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