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

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

Open Access

Some 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) - uniqueness , mathematics , contraction (grammar) , nonlinear system , type (biology) , boundary value problem , contraction mapping , mathematical analysis , contraction principle , 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).

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