Positive solutions for nonlinear Hadamard fractional differential equations with integral boundary conditions

Abdelouaheb Ardjouni; Abdelouaheb Ardjouni

doi:10.3934/math.2019.4.1101

AIMS Mathematics

2019, Volume 4, Issue 4: 1101-1113. doi: 10.3934/math.2019.4.1101

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Research article

Positive solutions for nonlinear Hadamard fractional differential equations with integral boundary conditions

Abdelouaheb Ardjouni ^,

Faculty of Sciences and Technology, Department of Mathematics and Informatics, University of Souk Ahras, P. O. Box 1553, Souk Ahras, 41000, Algeria

Received: 07 April 2019 Accepted: 25 July 2019 Published: 12 August 2019
MSC : 26A33, 34A12, 34G20

In this paper, we prove the existence and uniqueness of a positive solution of nonlinear Hadamard fractional differential equations with integral boundary conditions. In the process we employ the Schauder and Banach fixed point theorems and the method of upper and lower solutions to show the existence and uniqueness of a positive solution. Finally, an example is given to illustrate our results.
- fractional differential equations,
- positive solutions,
- upper and lower solutions,
- existence,
- uniqueness,
- fixed point theorems
Citation: Abdelouaheb Ardjouni. Positive solutions for nonlinear Hadamard fractional differential equations with integral boundary conditions[J]. AIMS Mathematics, 2019, 4(4): 1101-1113. doi: 10.3934/math.2019.4.1101

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Abstract

In this paper, we prove the existence and uniqueness of a positive solution of nonlinear Hadamard fractional differential equations with integral boundary conditions. In the process we employ the Schauder and Banach fixed point theorems and the method of upper and lower solutions to show the existence and uniqueness of a positive solution. Finally, an example is given to illustrate our results.

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