Application of the fixed point theorems on the existence  of solutions for <em>q-</em>fractional boundary value problems

Sina Etemad; Sotiris K. Ntouyas; Sina Etemad; Sotiris K. Ntouyas

doi:10.3934/math.2019.3.997

AIMS Mathematics

2019, Volume 4, Issue 3: 997-1018. doi: 10.3934/math.2019.3.997

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Application of the fixed point theorems on the existence of solutions for q-fractional boundary value problems

Sina Etemad ¹,
Sotiris K. Ntouyas ^{2,3
,
,}

1.
Department of Mathematics, Azarbaijan Shahid Madani University, Azarshahr, Tabriz, Iran
2.
Department of Mathematics, University of Ioannina, 451 10 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

Received: 30 May 2019 Accepted: 02 July 2019 Published: 31 July 2019
MSC : 34A08, 34A60, 39A12, 39A13

In this paper, we study the existence of solutions for nonlinear fractional q-difference equations and inclusions. We apply some known fixed point theorems to prove the existence results. Finally, some illustrative examples are presented to state the validity of our main results.
- fractional q-difference equation and inclusion,
- boundary value problem,
- existence,
- fixed point theorem
Citation: Sina Etemad, Sotiris K. Ntouyas. Application of the fixed point theorems on the existence of solutions for q-fractional boundary value problems[J]. AIMS Mathematics, 2019, 4(3): 997-1018. doi: 10.3934/math.2019.3.997

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Abstract

In this paper, we study the existence of solutions for nonlinear fractional q-difference equations and inclusions. We apply some known fixed point theorems to prove the existence results. Finally, some illustrative examples are presented to state the validity of our main results.

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