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 Monotone Iterative Technique and Ulam-Hyers Stability Analysis for Nonlinear Fractional Order Differential Equations with Integral Boundary Value Conditions

2019 ◽  
Vol 12 (2) ◽  
pp. 432-447
Author(s):  
Sajjad Ali ◽  
Kamal Shah ◽  
Hassan Khan ◽  
Muhammad Arif ◽  
Shahid Mahmood
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Iterative Scheme ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Extremal Solutions ◽  
Integral Boundary ◽  
Monotone Iterative ◽  
Fractional Differential

In this manuscript, the monotone iterative scheme has been extended to the nature of solution to boundary value problem of fractional differential equation that consist integral boundary conditions. In this concern, some sufficient conditions are developed in this manuscript. On the base of sufficient conditions, the monotone iterative scheme combined with lower and upper solution method for the existence, uniqueness, error estimates and various view plots of the extremal solutions to boundary value problem of nonlinear fractional differential equations have been studied. The obtain results have clarified the nature of the extremal solutions. Further, the Ulam--Hyers and Ulam--Hyers--Rassias stability have been investigated for the considered problem.  Two illustrative examples of the BVP of the nonlinear fractional differential equations have been provided to justify our contribution.

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 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>

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