On the generalized fractional Hankel transforms of arbitrary order in the Zemanian spaces

Abstract

In this paper, we introduce the fractional Hankel transform in Zemanian spaces H_μ, the space of test functions and in its dual H_μ^’, the space of distributions of slow growth, for any real value μ. Moreover, we prove some of its properties. As application, we solve some differential equations to illustrate the theoretical results and the importance of using this transform.