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

2021 ◽  
Vol 6 (11) ◽  
pp. 12718-12742
Author(s):  
Naeem Saleem ◽  
◽  
Mi Zhou ◽  
Shahid Bashir ◽  
Syed Muhammad Husnine ◽  
...  
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Integral Boundary ◽  
Integral Boundary Value Problem ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential ◽  
Contraction Type ◽  
Fractional Type

<abstract><p>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).</p></abstract>

scholarly journals Some New Existence and Uniqueness Results for an Integral Boundary Value Problem of Caputo Fractional Differential Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-11
Author(s):  
Haixing Feng ◽  
Chengbo Zhai
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Integral Boundary ◽  
Integral Boundary Value Problem ◽  
Uniqueness Results ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential

In this work, we consider an integral boundary value problem of Caputo fractional differential equations. Based on a fixed-point theorem of generalized concave operators, we obtain the existence and uniqueness of positive solutions. As applications of main results, we give two examples in the end.

scholarly journals An Integral Boundary Value Problem of Fractional Differential Equations with a Sign-Changed Parameter in Banach Spaces

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Chen Yang ◽  
Yaru Guo ◽  
Chengbo Zhai
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Banach Spaces ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Uniqueness Of Solutions ◽  
Integral Boundary ◽  
Integral Boundary Value Problem ◽  
Monotone Iterative ◽  
Fractional Differential

This paper is to investigate the existence and uniqueness of solutions for an integral boundary value problem of new fractional differential equations with a sign-changed parameter in Banach spaces. The main used approach is a recent fixed point theorem of increasing Ψ − h , r -concave operators defined on ordered sets. In addition, we can present a monotone iterative scheme to approximate the unique solution. In the end, two simple examples are given to illustrate our main results.

The method of upper and lower solutions for integral boundary value problem of semilinear fractional differential equations with non-instantaneous impulses

2020 ◽  
Vol 70 (3) ◽  
pp. 625-640 ◽  
Author(s):  
Mengrui Xu ◽  
Shurong Sun ◽  
Zhenlai Han
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Upper And Lower Solutions ◽  
Existence Results ◽  
Three Solutions ◽  
Integral Boundary ◽  
Integral Boundary Value Problem ◽  
Fractional Differential

AbstractIn this paper, we investigate a class of semilinear fractional differential equations with non-instantaneous impulses and integral boundary value conditions. By the method of upper and lower solutions combined with Amann three-solution theorem, existence results of at least three solutions are obtained.

scholarly journals Implicit nonlinear fractional differential equations of variable order

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Amar Benkerrouche ◽  
Mohammed Said Souid ◽  
Kanokwan Sitthithakerngkiet ◽  
Ali Hakem
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Variable Order ◽  
Stability Of Solutions ◽  
Nonlinear Fractional Differential Equations ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential ◽  
The Stability

AbstractIn this manuscript, we examine both the existence and the stability of solutions to the implicit boundary value problem of Caputo fractional differential equations of variable order. We construct an example to illustrate the validity of the observed results.

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