On the Generalized ( p, q )- ϕ -Calculus with Respect to Another Function

Sina Etemad, Ivanka Stamova (), Sotiris K. Ntouyas and Jessada Tariboon ()
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Sina Etemad: Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 3751-71379, Iran
Ivanka Stamova: Department of Mathematics, University of Texas at San Antonio, San Antonio, TX 78249, USA
Sotiris K. Ntouyas: Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece
Jessada Tariboon: Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand

Mathematics, 2024, vol. 12, issue 20, 1-24

Abstract: In the present paper, we generalized some of the operators defined in ( p , q ) -calculus with respect to another function. More precisely, the generalized ( p , q ) - ϕ -derivatives and ( p , q ) - ϕ -integrals were introduced with respect to the strictly increasing function ϕ with the help of different orders of the q -shifting, p -shifting, and ( q / p ) -shifting operators. Then, after proving some related properties, and as an application, we considered a generalized ( p , q ) - ϕ -difference problem and studied the existence property for its unique solutions with the help of the Banach contraction mapping principle.

Keywords: ( p , q )- ? -derivative; ( p , q )- ? -integral; ( q / p )-shifting operator; q -operator; existence of solution; boundary value problem; difference equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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