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.
