Distributional Representation of a Special Fox-Wright Function with an Application

A review of the literature demonstrates that the Fox-Wright function is not only a mathematical puzzle, but its role is naturally to represent basic physical phenomena. Motivated by this fact, we studied a new representation of this function in terms of complex delta functions. This representation was useful to compute its Laplace transform with respect to the third parameter & gamma; for which it also generalizes the one and two-parameter Mittag-Leffler functions. New identities involving the Fox-Wright function were discussed and used to simplify the results. Different fractional transforms were evaluated and the solution of a fractional kinetic equation was obtained by using its new representation. Several new properties of this function were discussed as a distribution.