Sonine Transform Associated to the Bessel-Struve Operator

In this paper we consider the Bessel-Struve operator \(l_\alpha\) and the Bessel-Struve intertwining operator \(\chi_\alpha\) and its dual, we define and study the Bessel-Struve Sonine transform \(S_{\alpha,\beta}\) on \(\mathcal{E}(\mathbb{R})\). We prove that \(S_{\alpha,\beta}\) is a transmutation operator from \(l_\alpha\) into \(l_\beta\) on \(\mathcal{E}(\mathbb{R})\) and we deduce similar result for its dual \(S_{\alpha,\beta}^*\) on \(\mathcal{E}'(\mathbb{R})\). Furthermore, invoking Weyl integral transform and the Dual Sonine transform \(^tS_{\alpha,\beta}\) on \(\mathcal{D}(\mathbb{R})\), we get a relation between the Bessel-Struve transforms \(\mathcal{F}^\alpha_{BS} \) and \(\mathcal{F}^\beta_{BS} \).