scholarly journals Monotone iterative technique for boundary value problems of a nonlinear fractional differential equation with deviating arguments

2012 ◽  
Vol 236 (9) ◽  
pp. 2425-2430 ◽  
Author(s):  
Guotao Wang
Keyword(s):  
Differential Equation ◽  
Boundary Value Problems ◽  
Fractional Differential Equation ◽  
Boundary Value ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Nonlinear Fractional Differential Equation ◽  
Deviating Arguments ◽  
Monotone Iterative ◽  
Fractional Differential

Monotone domain decomposition iterative technique for boundary value problems of a nonlinear fractional differential equation

2019 ◽  
Vol 12 (01) ◽  
pp. 1950011
Author(s):  
Myong-Gil Rim ◽  
Chol-Guk Choe
Keyword(s):  
Differential Equation ◽  
Domain Decomposition ◽  
Boundary Value Problems ◽  
Fractional Differential Equation ◽  
Boundary Value ◽  
Upper And Lower Solutions ◽  
Iterative Technique ◽  
Nonlinear Fractional Differential Equation ◽  
Actual Solution ◽  
Fractional Differential

In this paper, we present a monotone domain decomposition iterative technique for boundary value problems of a nonlinear fractional differential equation. We construct two monotone domain decomposition sequences of upper and lower solutions which converge uniformly to the actual solution of the problem. The accuracy and efficiency of our new approach are demonstrated through two examples.

Monotone Iterative Technique for Periodic Boundary Value Problem of Fractional Differential Equation in Banach Spaces

2019 ◽  
Vol 20 (5) ◽  
pp. 595-599 ◽  
Author(s):  
Pengyu Chen ◽  
Yibo Kong
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Banach Spaces ◽  
Fractional Differential Equation ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Monotone Iterative ◽  
Fractional Differential

AbstractIn this paper, we are concerned with the periodic boundary value problem of fractional differential equations on ordered Banach spaces. By introducing a concept of upper and lower solutions, we construct a new monotone iterative technique for the periodic boundary value problems of fractional differential equation, and obtain the existence of solutions between lower and upper solutions.

scholarly journals Boundary value problems for fractional differential equation with causal operators

2016 ◽  
Vol 1 (1) ◽  
pp. 11-22 ◽  
Author(s):  
Jingfei Jiang ◽  
Dengqing Cao ◽  
Huatao Chen
Keyword(s):  
Differential Equation ◽  
Boundary Value Problems ◽  
Fractional Differential Equation ◽  
Solution Method ◽  
Boundary Value ◽  
Monotone Iterative ◽  
Lower And Upper Solution ◽  
Fractional Differential ◽  
Causal Operators ◽  
Theoretical Results

AbstractIn this paper, we study the two-point boundary value problems for fractional differential equation with causal operator. By lower and upper solution method and the monotone iterative technique, some results for the extremal solution and quasisolutions are obtained. At last, an example is given to demonstrate the validity of assumptions and theoretical results.

scholarly journals Existence Results and the Monotone Iterative Technique for Nonlinear Fractional Differential Systems with Coupled Four-Point Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Yujun Cui ◽  
Yumei Zou
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Upper And Lower Solutions ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Point Boundary ◽  
Differential Systems ◽  
Monotone Iterative ◽  
Fractional Differential Systems ◽  
Fractional Differential

By establishing a comparison result and using the monotone iterative technique combined with the method of upper and lower solutions, we investigate the existence of solutions for nonlinear fractional differential systems with coupled four-point boundary value problems.

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