Some new generalizations of $ F- $contraction type mappings that weaken certain conditions on Caputo fractional type differential equations

Naeem Saleem; Mi Zhou; Shahid Bashir; Syed Muhammad Husnine; Naeem Saleem; Mi Zhou; Shahid Bashir; Syed Muhammad Husnine

doi:10.3934/math.2021734

AIMS Mathematics

2021, Volume 6, Issue 11: 12718-12742. doi: 10.3934/math.2021734

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Research article

Some new generalizations of $ F- $contraction type mappings that weaken certain conditions on Caputo fractional type differential equations

1.
Department of Mathematics, University of Management and Technology, Lahore, Pakistan
2.
School of Science and Technology, University of Sanya, Sanya, Hainan, 572000, China
3.
National University of Computer and Emerging Sciences, Lahore Campus, 54700, Pakistan

Received: 17 May 2021 Accepted: 02 September 2021 Published: 06 September 2021
MSC : 47H10, 47H19, 54H25

In this paper, firstly, we introduce some new generalizations of $ F- $contraction, $ F- $Suzuki contraction, and $ F- $expanding mappings. Secondly, we prove the existence and uniqueness of the fixed points for these mappings. Finally, as an application of our main result, we investigate the existence of a unique solution of an integral boundary value problem for scalar nonlinear Caputo fractional differential equations with a fractional order (1, 2).
- generalized $ F- $contraction,
- generalized $ F- $Suzuki contraction,
- generalized $ F $-expanding mapping,
- fixed point
Citation: Naeem Saleem, Mi Zhou, Shahid Bashir, Syed Muhammad Husnine. Some new generalizations of $ F- $contraction type mappings that weaken certain conditions on Caputo fractional type differential equations[J]. AIMS Mathematics, 2021, 6(11): 12718-12742. doi: 10.3934/math.2021734

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Abstract

In this paper, firstly, we introduce some new generalizations of $ F- $contraction, $ F- $Suzuki contraction, and $ F- $expanding mappings. Secondly, we prove the existence and uniqueness of the fixed points for these mappings. Finally, as an application of our main result, we investigate the existence of a unique solution of an integral boundary value problem for scalar nonlinear Caputo fractional differential equations with a fractional order (1, 2).

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