The present paper aims to study theory for generalized Hankel-Clifford transformation on certain spaces of generalizedultradifferentiable functions. To extend the transform to a space of ultradistributions, the class of rapid descent ultra-differentiable functions are stated. Mappings involving various differential operators are investigated and stated to be continuous. The theory developed is applied to solve some partial differential equations involving generalized Kepsinki-type-operator with ultradistributional initial conditions.
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