Integral representations of products of airy functions related to fractional calculus

In this paper, using the inverse Laplace transform of multi-valued functions we show new identities for the powers of Airy functions in terms of the Riemann-Liouville and Weyl fractional integrals of order α .In this sense, we get new integral representations for the special functions including trigonometric functions in terms of the M-Wright function and Hilbert transform.Also, we get the Hadamard fractional integrals of Airy functions in terms of the Widder potential and Mellin transforms of the Volterra functions.