The generalized Hankel-Clifford transformation on M&#x2032;<inf>&#x03B1;</inf> and its representation

A perspective on fractional Laplace transforms and fractional generalized Hankel-Clifford transformation

“…E is a member of E ′ [4]. In order to extend the relation (2.2) to the space of distributions, considered a lemma to prove…”

“…Proof. Since the testing function space (h α,β f ) (ξ) , L (w, z) and L (w)are subspace of E , the space of distributions of compact support E ′ is a subspace of all the generalized function space z) and L ′ (w) [4]. Therefore the restriction of f ∈ L ′ (w) to L (w, z) is in z) to E is a member of E ′ .…”

“…The Laplace transform of a function of a function f (t) ∈ L (0, ∞) is defined by the equation [1] L (f ; p) = ∫ ∞ 0 e −pt f (t) dt ; (Re (p) > 0) (1.1) and Malgonde [4] investigated the variant of the generalized Hankel-Clifford transform defined by…”

A Relation between Laplace and Generalized Hankel-Clifford Transformation

“…E is a member of  E [4]. In order to extend the relation (3) to the space of distributions, a lemma is stated.…”