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

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).

[1]  S. Banach.  Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales , 1922 .

[2]  B. Sims,et al.  Mean Lipschitzian mappings. , 2010 .

[3]  E. Karapınar,et al.  Fixed Points of Generalized -Suzuki Type Contraction in Complete -Metric Spaces , 2015 .

[4]  Shujun Jiang,et al.  Fixed point theorems of JS-quasi-contractions , 2016 .

[5]  N. Mehmood,et al.  Existence results for fractional order boundary value problem with nonlocal non-separated type multi-point integral boundary conditions , 2020 .

[6]  Andor Lukács,et al.  Fixed point theorems for various types of F-contractions in complete b-metric spaces , 2018 .

[7]  Xiao-Bao Shu,et al.  A study on the mild solution of impulsive fractional evolution equations , 2016, Appl. Math. Comput..

[8]  Hoda A. Fouad,et al.  Generalized Fixed Point Results with Application to Nonlinear Fractional Differential Equations , 2020, Mathematics.

[9]  X. Shu,et al.  Existence of almost periodic solutions for fractional impulsive neutral stochastic differential equations with infinite delay , 2020, Stochastics and Dynamics.

[10]  Michael A. Geraghty,et al.  On contractive mappings , 1973 .

[11]  Francesca Vetro,et al.  F-contractions of Hardy–Rogers-type and application to multistage decision , 2016 .

[12]  A generalization of the Banach Contraction principle , 2002 .

[13]  A fixed point theorem by altering distance technique in complete metric spaces , 2013 .

[14]  Weak $F$-contractions and some fixed point results , 2016 .

[15]  Nicolae Adrian Secelean,et al.  Iterated function systems consisting of F-contractions , 2013, Fixed Point Theory and Applications.

[16]  L. Ceng,et al.  Hybrid inertial subgradient extragradient methods for variational inequalities and fixed point problems involving asymptotically nonexpansive mappings , 2019, Optimization.

[17]  Xiao-Bao Shu,et al.  The existence of mild solutions for impulsive fractional partial differential equations , 2011 .

[18]  X. Shu,et al.  The existence and Hyers-Ulam stability of solution for almost periodical fractional stochastic differential equation with fBm , 2020 .

[19]  Bessem Samet,et al.  A new generalization of the Banach contraction principle , 2014, Journal of Inequalities and Applications.

[20]  N. Saleem,et al.  Coincidence and fixed points of multivalued F-contractions in generalized metric space with application , 2020, Journal of Fixed Point Theory and Applications.

[21]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations , 2006 .

[22]  J. Górnicki.  Fixed point theorems for F-expanding mappings , 2016 .

[23]  Dariusz Wardowski,et al.  Fixed points of a new type of contractive mappings in complete metric spaces , 2012, Fixed Point Theory and Applications.

[24]  Poom Kumam,et al.  Some fixed point theorems concerning F-contraction in complete metric spaces , 2014, Fixed Point Theory and Applications.

[25]  Petko D. Proinov.  Fixed point theorems for generalized contractive mappings in metric spaces , 2020 .

[26]  S. Moradi.  Fixed point of single-valued cyclic weak φF-contraction mappings , 2014 .

[27]  $${\psi F}$$ψF-Contractions: Not Necessarily Nonexpansive Picard Operators , 2016 .

[28]  N. Dung,et al.  Fixed Points Of F-Weak Contractions On Complete Metric Spaces , 2014 .

[29]  A. Petruşel,et al.  Two inertial subgradient extragradient algorithms for variational inequalities with fixed-point constraints , 2020 .