scholarly journals The existence of a solution for a fractional differential equation with nonlinear boundary conditions considered using upper and lower solutions in reverse order

2011 ◽  
Vol 62 (3) ◽  
pp. 1269-1274 ◽  
Author(s):  
Shuqin Zhang ◽  
Xinwei Su
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Fractional Differential Equation ◽  
Nonlinear Boundary ◽  
Upper And Lower Solutions ◽  
Nonlinear Boundary Conditions ◽  
Reverse Order ◽  
Existence Of A Solution ◽  
Fractional Differential

scholarly journals Monotone Iterative Method for ψ-Caputo Fractional Differential Equation with Nonlinear Boundary Conditions

2021 ◽  
Vol 5 (3) ◽  
pp. 81
Author(s):  
Zidane Baitiche ◽  
Choukri Derbazi ◽  
Jehad Alzabut ◽  
Mohammad Esmael Samei ◽  
Mohammed K. A. Kaabar ◽  
...  
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Fractional Differential Equation ◽  
Nonlinear Boundary ◽  
Upper And Lower Solutions ◽  
Nonlinear Boundary Conditions ◽  
Monotone Iterative Technique ◽  
Monotone Iterative Method ◽  
Monotone Iterative ◽  
Fractional Differential

The main contribution of this paper is to prove the existence of extremal solutions for a novel class of ψ-Caputo fractional differential equation with nonlinear boundary conditions. For this purpose, we utilize the well-known monotone iterative technique together with the method of upper and lower solutions. Finally, we provide an example along with graphical representations to confirm the validity of our main results.

Multiple Solutions of Nonlinear Fractional Differential Equations with p-Laplacian Operator and Nonlinear Boundary Conditions

2015 ◽  
Vol 65 (1) ◽  
Author(s):  
Yiliang Liu ◽  
Liang Lu
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Multiple Solutions ◽  
Nonlinear Boundary ◽  
Upper And Lower Solutions ◽  
Nonlinear Boundary Conditions ◽  
Laplacian Operator ◽  
Nonlinear Fractional Differential Equations ◽  
Fractional Differential

AbstractIn this paper, we deal with multiple solutions of fractional differential equations with p-Laplacian operator and nonlinear boundary conditions. By applying the Amann theorem and the method of upper and lower solutions, we obtain some new results on the multiple solutions. An example is given to illustrate our results.

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