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The main objective of this paper is to study the fractional generalized Hankel-Clifford transformation and some of their basic properties. The continuous fractional generalized Hankel-Clifford transformation, its inversion formula are also studied. The finite continuous fractional generalized Hankel-Clifford transformation is also studied in Zemanian space. Applications of the finite fractional generalized Hankel-Clifford transformation in solving generalized n th order linear non-homogeneous partial differential equation is given.
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