Method of upper and lower solutions for coupled system of nonlinear fractional integro-differential equations with advanced arguments

2017 ◽  
Vol 67 (1) ◽  
pp. 89-98
Author(s):  
Neda Khodabakhshi ◽  
S. Mansour Vaezpour ◽  
J. Juan Trujillo
Keyword(s):  
Differential Equations ◽  
Iterative Method ◽  
Upper And Lower Solutions ◽  
Coupled System ◽  
Extremal Solutions ◽  
Monotone Iterative Method ◽  
Monotone Iterative

AbstractIn this paper, by means of upper and lower solutions, we develop monotone iterative method for the existence of extremal solutions for coupled system of nonlinear fractional integro-differential equations with advanced arguments. We illustrate this technique with the help of an example.

scholarly journals A monotone iterative method for boundary value problems of parametric differential equations

2001 ◽  
Vol 14 (2) ◽  
pp. 183-187 ◽  
Author(s):  
Xinzhi Liu ◽  
Farzana A. McRae
Keyword(s):  
Differential Equations ◽  
Iterative Method ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Upper And Lower Solutions ◽  
Extremal Solutions ◽  
Monotone Iterative Method ◽  
Monotone Iterative ◽  
Monotone Sequences

This paper studies boundary value problems for parametric differential equations. By using the method of upper and lower solutions, monotone sequences are constructed and proved to converge to the extremal solutions of the boundary value problem.

SUCCESSIVE ITERATIONS FOR POSITIVE EXTREMAL SOLUTIONS OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS ON A HALF-LINE

2014 ◽  
Vol 91 (1) ◽  
pp. 116-128 ◽  
Author(s):  
LIHONG ZHANG ◽  
BASHIR AHMAD ◽  
GUOTAO WANG
Keyword(s):  
Differential Equations ◽  
Iterative Method ◽  
Fractional Differential Equations ◽  
Lower Order ◽  
Extremal Solutions ◽  
Half Line ◽  
Monotone Iterative Method ◽  
Iterative Schemes ◽  
Monotone Iterative ◽  
Fractional Differential

AbstractIn this paper, positive solutions of fractional differential equations with nonlinear terms depending on lower-order derivatives on a half-line are investigated. The positive extremal solutions and iterative schemes for approximating them are obtained by applying a monotone iterative method. An example is presented to illustrate the main results.

Monotone iterative method for a class of nonlinear fractional differential equations

2012 ◽  
Vol 15 (2) ◽  
Author(s):  
Guotao Wang ◽  
Dumitru Baleanu ◽  
Lihong Zhang
Keyword(s):  
Differential Equations ◽  
Iterative Method ◽  
Fractional Differential Equations ◽  
Monotone Iterative Technique ◽  
Monotone Iterative Method ◽  
Iterative Technique ◽  
Nonlinear Fractional Differential Equations ◽  
Monotone Iterative ◽  
Liouville Fractional Derivative ◽  
Fractional Differential

AbstractBy applying the monotone iterative technique and the method of lower and upper solutions, this paper investigates the existence of extremal solutions for a class of nonlinear fractional differential equations, which involve the Riemann-Liouville fractional derivative D q x(t). A new comparison theorem is also build. At last, an example is given to illustrate our main results.

Analysis of a system of autonomous fractional differential equations

2017 ◽  
Vol 10 (07) ◽  
pp. 1750094 ◽  
Author(s):  
Xiaojun Zhou ◽  
Chuanju Xu
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Upper And Lower Solutions ◽  
Coupled System ◽  
Monotone Iterative Technique ◽  
Metapopulation Model ◽  
Uniqueness Of Solutions ◽  
Predator Prey ◽  
Monotone Iterative ◽  
Fractional Differential

In this work, we study a system of autonomous fractional differential equations. The differential operator is taken in the Caputo sense. Using the monotone iterative technique combined with the method of upper and lower solutions, we investigate the existence and uniqueness of solutions for coupled system which are nonlinear fractional differential equations, moreover, we obtain the dependence of the solution on the initial values. In addition, we give an important example that is a two-patch subdiffusive predator–prey metapopulation model, investigate the solvability and give the numerical results with this model. The numerical simulation indicates that the results of the subdiffusive model approximate to the two-patch predator–prey metapopulation model with the order [Formula: see text] approach to 1.

scholarly journals Monotone iterative solutions for a coupled system of p-Laplacian differential equations involving the Riemann–Liouville fractional derivative

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Bo Bi ◽  
Ying He
Keyword(s):  
Differential Equations ◽  
Upper And Lower Solutions ◽  
Integral Boundary Conditions ◽  
Coupled System ◽  
Monotone Iterative Technique ◽  
Integral Boundary ◽  
Monotone Iterative ◽  
Coupled Integral Boundary Conditions ◽  
Liouville Fractional Derivative ◽  
Iterative Solutions

AbstractApplying the monotone iterative technique and the method of upper and lower solutions, we investigate the existence of extremal solutions for a nonlinear system of p-Laplacian differential equations with nonlocal coupled integral boundary conditions. We present a numerical example to illustrate the main result.

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