Geodesic
q-Heat Operator and q-Poisson’s Operator
Fractional calculus and applied analysis, Tome 9 (2006) no. 3, pp. 265-286.

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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.
Keywords: q-Special Functions, q-Operators, q-Transforms, q-Heat Equation, 33D15, 33D90, 39A13 
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Mabrouk, Hanène. q-Heat Operator and q-Poisson’s Operator. Fractional calculus and applied analysis, Tome 9 (2006) no. 3, pp. 265-286. http://geodesic.mathdoc.fr/item/FCAA_2006_9_3_a4/