Open AccessSome new generalizations of $ F- $contraction type mappings that weaken certain conditions on Caputo fractional type differential equations
Author(s) -
Naeem Saleem,
Mi Zhou,
Shahid Bashir,
Syed Muhammad Husnine
Publication year - 2021
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2021734
Subject(s) - mathematics , uniqueness , contraction (grammar) , nonlinear system , contraction mapping , contraction principle , type (biology) , boundary value problem , mathematical analysis , pure mathematics , scalar (mathematics) , fixed point , physics , geometry , medicine , ecology , quantum mechanics , biology
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).