Airy functions and Riesz fractional trigonometric operators. Issue 8 (3rd August 2018)

• Record Type: Journal Article
• Authors: Askari, Hassan; Ansari, Alireza
• Is Part Of: Integral transforms and special functions. Volume 29:Issue 8(2018)
• Page Start: 585
• Page End: 604
• Publication Date: 2018-08-03
• Subjects: Airy functions -- Mellin transforms -- Riesz fractional derivatives -- addition formula -- Ostrovsky equation; 33C10 -- 44A20; Integral transforms -- Periodicals; Transcendental functions -- Periodicals; Transformations (Mathematics) -- Periodicals; Calculus, Integral -- Periodicals; 515
• DOI: 10.1080/10652469.2018.1472593
• Languages: English
• ISSNs: 1065-2469

Abstract

ABSTRACT: In this paper, using the Riesz fractional derivativeD := − d 2 / d x 2, we present the Mellin transforms of shifted Airy functions in terms of the Riesz fractional derivatives of Airy functions. We also show some integral addition formulas for the products of Airy functions in terms of the Riesz fractional trigonometric operators. Moreover, the fundamental solution of the Ostrovsky equation is given by the Riesz fractional trigonometric operators.