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In this paper, we get integral representations for the quintic Airy functions as the four linearly independent solutions of differential equation y (4) + xy = 0. Also, new integral representations for the products of these functions are obtained in terms of the Bessel functions and the Riesz fractional derivatives of these products are given.
Abstract
We present some relations for inequalities involving certain differential-integral operators.
. [ 15–16 ] investigated the efficiency of the installation of VEDs for reducing the resonant response of a short simply supported railway bridge. Tsai and Lee [ 17 ] developed a finite element model based on fractional derivatives in order to study the
(Institute of Physics) Conference Series: Materials Science and Engineering ( 2018 ), vol. 332 , p. 1 . [8] Antunes , P. R ., and Ferreira , R. A . Analysis of a class of boundary value problems depending on left and right Caputo fractional derivatives
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-9939-1988-0938668-8 . [8] Ditzian , Z. 1998 Fractional derivatives and best approximation Acta Math. Hungar. 81 323 – 348 10.1023/A:1006554907440
differential equations involving Riemann-Liouville sequential fractional derivative . J. Math. Anal. Appl ., 367 : 260 - 272 , 2010 . [9] X . Xu . Existence and multiplicity of positive solutions for multi-parameter three-point differential equations
