Abstract
In this paper we continue as in \cite{Rezguietal} to exploit the modified variants of Bessel function in the framework of $q$-theory to construct wavelet operators. A generalized $q$-Bessel type function has been introduced leading to an associated mother wavelet which in turns has induced a continuous wavelet transform. Finally, Plancherel/Parceval type relations have been proved. Such variants of wavelets permit in some sense to approximate solutions of ODEs and PDEs by transforming them to recurrent sequences.
Publisher
Sociedade Paranaense de Matemática
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