Monotone iterative method for nonlinear fractional p ‐Laplacian differential equation in terms of ψ ‐Caputo fractional derivative equipped with a new class of nonlinear boundary conditions

2021 ◽  
Author(s):  
Zidane Baitiche ◽  
Choukri Derbazi ◽  
Guotao Wang
Keyword(s):  
Differential Equation ◽  
Iterative Method ◽  
Boundary Conditions ◽  
Fractional Derivative ◽  
Caputo Fractional Derivative ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Monotone Iterative Method ◽  
New Class ◽  
Monotone Iterative

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.

scholarly journals Monotone iterative method for fractional p-Laplacian differential equations with four-point boundary conditions

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Xiaoping Li ◽  
Minyuan He
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Iterative Method ◽  
Boundary Conditions ◽  
Boundary Problem ◽  
Positive Solutions ◽  
Monotone Iterative Method ◽  
Point Boundary ◽  
Abstract Result ◽  
Monotone Iterative

AbstractA four-point boundary problem for a fractional p-Laplacian differential equation is studied. The existence of two positive solutions is established by means of the monotone iterative method. An example supporting the abstract result is given.

Ordinary Differential Equations with Nonlinear Boundary Conditions

2002 ◽  
Vol 9 (2) ◽  
pp. 287-294
Author(s):  
Tadeusz Jankowski
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Existence Results ◽  
Monotone Iterative Technique ◽  
Lower And Upper Solutions ◽  
Iterative Technique ◽  
Monotone Iterative

Abstract The method of lower and upper solutions combined with the monotone iterative technique is used for ordinary differential equations with nonlinear boundary conditions. Some existence results are formulated for such problems.

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