Abstract: The fractional Hankel transform which is a generalization of the Hankel transform has many applications. In this paper we establish the initial and final value theorem for the generalized fractional Hankel transform. Keywords: Fourier transform, Hankel transform, fractional Hankel transform. I. Introduction: Namias [1 , 2] introduced the concept of Fourier transform of fractional order by the method of eigen values and open the path of defining the number of fractional integral transform having applications in quantum mechanics [1], Optics [3] and Signal processing [4]. Hankel transform is also generalized to its fractional version. Namias [2] himself has presented the formula for fractional Hankel transform as � ∝ � =� , � � −𝑖+𝑣1 ∝�2−𝛼2 �𝑖� 𝛼2 �� − 𝑖2 � 2 +� ��� 2 ∞� � 𝑣 ���𝑖� ∝2 � � ��Which is a generalization of Hankel transform, � ∝ � � = .� �� � � 𝑣 �� �� ∞� Kerr [5] introduced the fractional Hankel transform as, �