A convolution family in the Dimovski sense for the composed Erdélyi-Kober fractional integrals. Issue 5 (4th May 2019)

• Record Type: Journal Article
• Authors: Al-Kandari, M.; Hanna, L. A.-M.; Luchko, Yu. F.
• Is Part Of: Integral transforms and special functions. Volume 30:Issue 5(2019)
• Page Start: 400
• Page End: 417
• Publication Date: 2019-05-04
• Subjects: Erdélyi-Kober fractional integrals and derivatives -- Caputo-type Erdélyi-Kober derivative -- Mellin-Barnes integral representations -- convolutions in the Dimovski sense; 26A33 -- 44A40 -- 44A35 -- 33E30 -- 45J05; Integral transforms -- Periodicals; Transcendental functions -- Periodicals; Transformations (Mathematics) -- Periodicals; Calculus, Integral -- Periodicals; 515
• DOI: 10.1080/10652469.2019.1576037
• Languages: English
• ISSNs: 1065-2469

Abstract

ABSTRACT: In this paper, we first introduce suitable compositions of the right- and left-hand sided Erdélyi-Kober fractional integrals and derivatives that we call composed Erdélyi-Kober fractional integrals and derivatives. These operators play an important role while treating the fractional differential equations containing both the right- and the left-hand sided Erdélyi-Kober fractional derivatives. One of possible strategies for solving these equations is to apply a kind of operational calculus for the composed Erdélyi-Kober fractional derivatives. The first step in development of such operational calculus in Mikusiński sense consists in construction of a suitable convolution. In this paper, a one-parametric family of convolutions in the Dimovski sense for the composed Erdélyi-Kober fractional integrals is constructed.