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.

Automated summary

A literature review reveals that the Fox-Wright function serves as more than a mere mathematical puzzle, as it naturally represents fundamental physical phenomena. Motivated by this insight, we explore a new representation of the function using complex delta functions. This representation proves useful for computing the Laplace transform of the function with respect to the third parameter γ, and it extends the one and two-parameter Mittag-Leffler functions. New identities involving the Fox-Wright function are discussed and utilized to simplify the obtained results. Additionally, we evaluate various fractional transforms and apply the new representation to obtain the solution for a fractional kinetic equation. Several new properties of the function are studied as a distribution.