scholarly journals Extremal Solutions for Caputo Conformable Differential Equations with p-Laplacian Operator and Integral Boundary Condition

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Zhongqi Peng ◽  
Yuan Li ◽  
Qi Zhang ◽  
Yimin Xue
Keyword(s):  
Extremal Solutions ◽  
Laplacian Operator ◽  
Banach Fixed Point Theorem ◽  
Conformable Derivative ◽  
Integral Boundary ◽  
Monotone Iterative ◽  
Fractional Differential Operator ◽  
Conformable Derivatives ◽  
Uniqueness Of The Solution ◽  
Fractional Differential

The Caputo conformable derivative is a new Caputo-type fractional differential operator generated by conformable derivatives. In this paper, using Banach fixed point theorem, we obtain the uniqueness of the solution of nonlinear and linear Cauchy problem with the conformable derivatives in the Caputo setting, respectively. We also establish two comparison principles and prove the extremal solutions for nonlinear fractional p -Laplacian differential system with Caputo conformable derivatives by utilizing the monotone iterative technique. An example is given to verify the validity of the results.

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 Existence and iteration of positive solution for fractional integral boundary value problems with p-Laplacian operator

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Ying He ◽  
Bo Bi
Keyword(s):  
Boundary Value ◽  
Upper And Lower Solutions ◽  
Sufficient Conditions ◽  
Monotone Iterative Technique ◽  
Laplacian Operator ◽  
Integral Boundary ◽  
Monotone Iterative ◽  
Fractional Differential ◽  
Integral Boundary Value Problems ◽  
The Given

Abstract This paper is concerned with an integral boundary value problem of fractional differential equations with p-Laplacian operator. Sufficient conditions ensuring the existence of extremal solutions for the given problem are obtained. Our results are based on the method of upper and lower solutions and monotone iterative technique.

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.

scholarly journals Monotone Iterative Technique for Conformable Fractional Differential Equations with Deviating Arguments

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Huiling Chen ◽  
Shuman Meng ◽  
Yujun Cui
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Sufficient Conditions ◽  
Monotone Iterative Technique ◽  
Extremal Solutions ◽  
Iterative Technique ◽  
Deviating Arguments ◽  
Comparison Principles ◽  
Monotone Iterative ◽  
Fractional Differential

This paper is concerned with the existence of extremal solutions for periodic boundary value problems for conformable fractional differential equations with deviating arguments. We first build two comparison principles for the corresponding linear equation with deviating arguments. With the help of new comparison principles, some sufficient conditions for the existence of extremal solutions are established by combining the method of lower and upper solutions and the monotone iterative technique. As an application, an example is presented to enrich the main results of this article.

scholarly journals Existence of Solutions for Fractional Differential Equations with p-Laplacian Operator and Integral Boundary Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Jingli Xie ◽  
Lijing Duan
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence Of Solutions ◽  
Integral Boundary Conditions ◽  
Laplacian Operator ◽  
Integral Boundary ◽  
Fractional Differential ◽  
Integral Boundary Value Problems ◽  
The Fixed Point Theorem

In this paper, we investigate a class of integral boundary value problems of fractional differential equations with a p-Laplacian operator. Existence of solutions is obtained by using the fixed point theorem, and an example is given to show the applicability of our main result.

scholarly journals Existence Results for a Class of p-Laplacian Fractional Differential Equations with Integral Boundary Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
SunAe Pak ◽  
KumSong Jong ◽  
KyuNam O ◽  
HuiChol Choi
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Integral Boundary Conditions ◽  
Contraction Mapping Principle ◽  
Laplacian Operator ◽  
Uniqueness Of Solutions ◽  
Integral Boundary ◽  
Uniqueness Results ◽  
Fractional Differential

In this paper, we investigate the existence and uniqueness of solutions for a class of integral boundary value problems of nonlinear fractional differential equations with p-Laplacian operator. We obtain some existence and uniqueness results concerned with our problem by using Schaefer’s fixed-point theorem and Banach contraction mapping principle. Finally, we present some examples to illustrate our main results.

scholarly journals Monotone iterative schemes for positive solutions of a fractional differential system with integral boundary conditions on an infinite interval

Filomat ◽  
2020 ◽  
Vol 34 (13) ◽  
pp. 4399-4417
Author(s):  
Yaohong Li ◽  
Wei Cheng ◽  
Jiafa Xu
Keyword(s):  
Positive Solutions ◽  
Differential System ◽  
Integral Boundary Conditions ◽  
Contraction Mapping Principle ◽  
Infinite Interval ◽  
Integral Boundary ◽  
Iterative Schemes ◽  
Monotone Iterative ◽  
Fractional Differential System ◽  
Fractional Differential

In this paper, using the monotone iterative technique and the Banach contraction mapping principle, we study a class of fractional differential system with integral boundary on an infinite interval. Some explicit monotone iterative schemes for approximating the extreme positive solutions and the unique positive solution are constructed.

scholarly journals Local existence–uniqueness and monotone iterative approximation of positive solutions for p-Laplacian differential equations involving tempered fractional derivatives

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Bibo Zhou ◽  
Lingling Zhang
Keyword(s):  
Positive Solution ◽  
Local Existence ◽  
Monotone Operators ◽  
Unique Positive Solution ◽  
Iterative Approximation ◽  
Integral Boundary ◽  
Monotone Iterative ◽  
Fractional Differential ◽  
Integral Boundary Value Problems ◽  
Laplacian Operators

AbstractIn this paper, we are concerned with a kind of tempered fractional differential equation Riemann–Stieltjes integral boundary value problems with p-Laplacian operators. By means of the sum-type mixed monotone operators fixed point theorem based on the cone $P_{h}$ P h , we obtain not only the local existence with a unique positive solution, but also construct two successively monotone iterative sequences for approximating the unique positive solution. Finally, we present an example to illustrate our main results.

scholarly journals New Existence and Uniqueness Results for Fractional Differential Equations

2013 ◽  
Vol 21 (3) ◽  
pp. 33-42 ◽  
Author(s):  
Ahmed Anber ◽  
Soumia Belarbi
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Integral Boundary Conditions ◽  
Existence Results ◽  
Banach Fixed Point Theorem ◽  
Integral Boundary ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential

AbstractIn this paper, we study a class of boundary value problems of nonlinear fractional differential equations with integral boundary conditions. Some new existence and uniqueness results are obtained by using Banach fixed point theorem. Other existence results are also presented by using Krasnoselskii theorem.

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