Impulsive Boundary Value Problems for Two Classes of Fractional Differential Equation with Two Different Caputo Fractional Derivatives

2015 ◽  
Vol 13 (3) ◽  
pp. 1033-1050 ◽  
Author(s):  
Kaihong Zhao
Keyword(s):  
Differential Equation ◽  
Boundary Value Problems ◽  
Fractional Differential Equation ◽  
Fractional Derivatives ◽  
Boundary Value ◽  
Caputo Fractional Derivatives ◽  
Impulsive Boundary Value Problems ◽  
Fractional Differential

scholarly journals Existence and Nonexistence of Positive Solutions for Fractional Three-Point Boundary Value Problems with a Parameter

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Yunhong Li ◽  
Weihua Jiang
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Fractional Differential Equation ◽  
Positive Solutions ◽  
Boundary Value ◽  
Point Boundary ◽  
Existence And Nonexistence ◽  
Fractional Differential

In this work, we investigate the existence and nonexistence of positive solutions for p-Laplacian fractional differential equation with a parameter. On the basis of the properties of Green’s function and Guo-Krasnosel’skii fixed point theorem on cones, the existence and nonexistence of positive solutions are obtained for the boundary value problems. We also give some examples to illustrate the effectiveness of our main results.

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.

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