Existence Theory for a Fractional q -Integro-Difference Equation with q -Integral Boundary Conditions of Different Orders

Sina Etemad, Sotiris K. Ntouyas and Bashir Ahmad
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Sina Etemad: Department of Mathematics, Azarbaijan Shahid Madani University, Azarshahr, Tabriz, Iran
Sotiris K. Ntouyas: Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece
Bashir Ahmad: Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Mathematics, 2019, vol. 7, issue 8, 1-15

Abstract: In this paper, we study the existence of solutions for a new class of fractional q -integro-difference equations involving Riemann-Liouville q -derivatives and a q -integral of different orders, supplemented with boundary conditions containing q -integrals of different orders. The first existence result is obtained by means of Krasnoselskii’s fixed point theorem, while the second one relies on a Leray-Schauder nonlinear alternative. The uniqueness result is derived via the Banach contraction mapping principle. Finally, illustrative examples are presented to show the validity of the obtained results. The paper concludes with some interesting observations.

Keywords: q -integro-difference equation; boundary value problem; existence; fixed point (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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