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Article

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

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Department of Mathematics, Azarbaijan Shahid Madani University, Azarshahr, Tabriz, Iran
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Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece
3
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
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(8), 659; https://doi.org/10.3390/math7080659
Received: 18 June 2019 / Revised: 13 July 2019 / Accepted: 20 July 2019 / Published: 24 July 2019
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. View Full-Text
Keywords: q-integro-difference equation; boundary value problem; existence; fixed point q-integro-difference equation; boundary value problem; existence; fixed point
MDPI and ACS Style

Etemad, S.; Ntouyas, S.K.; Ahmad, B. Existence Theory for a Fractional q-Integro-Difference Equation with q-Integral Boundary Conditions of Different Orders. Mathematics 2019, 7, 659. https://doi.org/10.3390/math7080659

AMA Style

Etemad S, Ntouyas SK, Ahmad B. Existence Theory for a Fractional q-Integro-Difference Equation with q-Integral Boundary Conditions of Different Orders. Mathematics. 2019; 7(8):659. https://doi.org/10.3390/math7080659

Chicago/Turabian Style

Etemad, Sina, Sotiris K. Ntouyas, and Bashir Ahmad. 2019. "Existence Theory for a Fractional q-Integro-Difference Equation with q-Integral Boundary Conditions of Different Orders" Mathematics 7, no. 8: 659. https://doi.org/10.3390/math7080659

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