Applications of fractional calculus (Q1101856)

By making use of the integral analogue of the generalized Leibniz rule and the generalized Lagrange expansion given by \textit{T. J. Osler} [Math. Comput. 26, 449-460 (1972; Zbl 0244.26004); ibid. 903-915 (1972; Zbl 0256.26006)] and some other known results in the theory of fractional calculus, the authors have obtained five infinite integrals, three Fourier transform pairs and two expansions in this paper. The results established herein appear to be interesting and involve the functions \(F_ 1\), \(\Phi_ 1\), Kampé de Fériet functions, Fox' H- function and the mutivariable H-function. A number of formulas involving simpler functions can be obtained as special cases of the main results established in this paper.