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We extend the semigroup {Φ λ } λ∈ℂ  of Gel’fand and Shilov to the semigroup {Φ λ } λ∈ℂ  n    and the one-dimensional fractional calculus of distributions to the case of distributions on Rn with supports in the nonnegative coneℝ  ¯    +  n$\overline{\mathbb{R}}_{+}^{n}$   . We use distributional mixed derivatives of an arbitrary complex order to solve Abel’s multidimensional integral equation and a distributional fractional differential equation of wave type.

Convolutional approach to fractional calculus for distributions of several variables