scholarly journals On a nonlinear mixed-order coupled fractional differential system with new integral boundary conditions

2021 ◽  
Vol 6 (6) ◽  
pp. 5801-5816
Author(s):  
Bashir Ahmad ◽  
◽  
Soha Hamdan ◽  
Ahmed Alsaedi ◽  
Sotiris K. Ntouyas ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Differential System ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Fractional Differential System ◽  
Mixed Order ◽  
Fractional Differential

scholarly journals Positive Solutions for(n-1,1)-Type Singular Fractional Differential System with Coupled Integral Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Ying Wang ◽  
Lishan Liu ◽  
Xinguang Zhang ◽  
Yonghong Wu
Keyword(s):  
Boundary Conditions ◽  
Positive Solutions ◽  
Differential System ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Fractional Differential System ◽  
Coupled Integral Boundary Conditions ◽  
Existence Of Positive Solutions ◽  
Singular Fractional Differential System ◽  
Fractional Differential

We study the positive solutions of the(n-1,1)-type fractional differential system with coupled integral boundary conditions. The conditions for the existence of positive solutions to the system are established. In addition, we derive explicit formulae for the estimation of the positive solutions and obtain the unique positive solution when certain additional conditions hold. An example is then given to demonstrate the validity of our main results.

scholarly journals The Existence Results of Solutions for System of Fractional Differential Equations with Integral Boundary Conditions

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Dongxia Zan ◽  
Run Xu
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Existence Of Solutions ◽  
Initial Point ◽  
Integral Boundary Conditions ◽  
Existence Results ◽  
Integral Boundary ◽  
Fractional Differential System ◽  
Fractional Differential

In this paper, we investigated the system of fractional differential equations with integral boundary conditions. By using a fixed point theorem in the Banach spaces, we get the existence of solutions for the fractional differential system. By constructing iterative sequences for any given initial point in space, we can approximate this solution. As an application, an example is presented 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 Positive solutions to n-dimensional $\alpha _{1}+\alpha _{2}$ order fractional differential system with p-Laplace operator

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Tian Wang ◽  
Guo Chen ◽  
Huihui Pang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Laplace Operator ◽  
Positive Solutions ◽  
Differential System ◽  
Integral Boundary Conditions ◽  
Existence Results ◽  
Integral Boundary ◽  
Fractional Differential System ◽  
Fractional Differential

AbstractIn this paper, we study an n-dimensional fractional differential system with p-Laplace operator, which involves multi-strip integral boundary conditions. By using the Leggett–Williams fixed point theorem, the existence results of at least three positive solutions are established. Besides, we also get the nonexistence results of positive solutions. Finally, two examples are presented to validate the main results.

scholarly journals Positive Solutions for Singularp-Laplacian Fractional Differential System with Integral Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Liping Wang ◽  
Zongfu Zhou ◽  
Hui Zhou
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Conditions ◽  
Positive Solutions ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Value System ◽  
Fractional Differential System ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

This paper investigates the existence of positive solutions for a class of singularp-Laplacian fractional differential equations with integral boundary conditions. By using the Leggett-Williams fixed point theorem, the existence of at least three positive solutions to the boundary value system is guaranteed.

scholarly journals Sequential Riemann–Liouville and Hadamard–Caputo Fractional Differential Systems with Nonlocal Coupled Fractional Integral Boundary Conditions

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 174
Author(s):  
Chanakarn Kiataramkul ◽  
Weera Yukunthorn ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Boundary Conditions ◽  
Fractional Integral ◽  
Integral Boundary Conditions ◽  
Contraction Mapping Principle ◽  
Uniqueness Of Solutions ◽  
Caputo Fractional Derivatives ◽  
Integral Boundary ◽  
Banach Contraction ◽  
Fractional Differential ◽  
Banach Contraction Mapping Principle

In this paper, we initiate the study of existence of solutions for a fractional differential system which contains mixed Riemann–Liouville and Hadamard–Caputo fractional derivatives, complemented with nonlocal coupled fractional integral boundary conditions. We derive necessary conditions for the existence and uniqueness of solutions of the considered system, by using standard fixed point theorems, such as Banach contraction mapping principle and Leray–Schauder alternative. Numerical examples illustrating the obtained results are also presented.

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