ON A FRACTIONAL q-INTEGRAL OPERATOR INVOLVING
THE BASIC ANALOGUE OF FOX-WRIGHT FUNCTION
Jaime Castillo1, Leda Galué2
1Researching Center, University of La Guajira
Faculty of Engineering, Block 6
Riohacha – 440002, COLOMBIA
2CIMA, University of Zulia
Maracaibo – 4001, VENEZUELA

Abstract

The fractional q-calculus is the q-extension of the ordinary fractional calculus. In the second half of the twentieth century there was a significant increase of activity in the area of the q-calculus due to its applications in mathematics and physics. Particularly, the operators of fractional calculus and their q-analogues have many applications. They can be used in crack problems in elasticity, in chaos theory, control systems, signal processing, bio-medical engineering, radars, sonars, etc. The aim of this paper is to define a new fractional q-integral operator of Kober type using the basic analogue of Fox-Wright function as kernel, and to establish a composition formula for a particular type of these operators. Also, some particular cases are obtained.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 33
Issue: 6
Year: 2020

DOI: 10.12732/ijam.v33i6.2

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