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).
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
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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