Maximal and minimal iterative positive solutions for $ p $-Laplacian Hadamard fractional differential equations with the derivative term contained in the nonlinear term

Limin Guo; Lishan Liu; Ying Wang; Limin Guo; Lishan Liu; Ying Wang

doi:10.3934/math.2021725

AIMS Mathematics

2021, Volume 6, Issue 11: 12583-12598. doi: 10.3934/math.2021725

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Maximal and minimal iterative positive solutions for $ p $-Laplacian Hadamard fractional differential equations with the derivative term contained in the nonlinear term

Limin Guo ^{1
,
,},
Lishan Liu ²,
Ying Wang ^{3
,
,}

1.
School of Science, Changzhou Institute of Technology, Changzhou 213002, China
2.
School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China
3.
School of Mathematicacs and Statistics, Linyi University, Linyi 276000, China

Received: 21 March 2021 Accepted: 07 June 2021 Published: 01 September 2021
MSC : 34B16, 34B18

In this paper, the maximal and minimal iterative positive solutions are investigated for a singular Hadamard fractional differential equation boundary value problem with a boundary condition involving values at infinite number of points. Green's function is deduced and some properties of Green's function are given. Based upon these properties, iterative schemes are established for approximating the maximal and minimal positive solutions.
- Hadamard fractional differential equation,
- iterative positive solution,
- positive solution,
- infinite-point
Citation: Limin Guo, Lishan Liu, Ying Wang. Maximal and minimal iterative positive solutions for $ p $-Laplacian Hadamard fractional differential equations with the derivative term contained in the nonlinear term[J]. AIMS Mathematics, 2021, 6(11): 12583-12598. doi: 10.3934/math.2021725

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Abstract

In this paper, the maximal and minimal iterative positive solutions are investigated for a singular Hadamard fractional differential equation boundary value problem with a boundary condition involving values at infinite number of points. Green's function is deduced and some properties of Green's function are given. Based upon these properties, iterative schemes are established for approximating the maximal and minimal positive solutions.

References

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