Monotone iterative technique for fractional differential equations with periodic boundary conditions

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.

Download Full-text

General uniqueness and monotone iterative technique for fractional differential equations

Applied Mathematics Letters ◽

10.1016/j.aml.2007.09.006 ◽

2008 ◽

Vol 21 (8) ◽

pp. 828-834 ◽

Cited By ~ 161

Author(s):

V. Lakshmikantham ◽

A.S. Vatsala

Keyword(s):

Differential Equations ◽

Fractional Differential Equations ◽

Monotone Iterative Technique ◽

Iterative Technique ◽

Monotone Iterative ◽

Fractional Differential

Download Full-text

Monotone Iterative Technique for Conformable Fractional Differential Equations with Deviating Arguments

Discrete Dynamics in Nature and Society ◽

10.1155/2020/5827127 ◽

2020 ◽

Vol 2020 ◽

pp. 1-9

Author(s):

Huiling Chen ◽

Shuman Meng ◽

Yujun Cui

Keyword(s):

Differential Equations ◽

Fractional Differential Equations ◽

Sufficient Conditions ◽

Monotone Iterative Technique ◽

Extremal Solutions ◽

Iterative Technique ◽

Deviating Arguments ◽

Comparison Principles ◽

Monotone Iterative ◽

Fractional Differential

This paper is concerned with the existence of extremal solutions for periodic boundary value problems for conformable fractional differential equations with deviating arguments. We first build two comparison principles for the corresponding linear equation with deviating arguments. With the help of new comparison principles, some sufficient conditions for the existence of extremal solutions are established by combining the method of lower and upper solutions and the monotone iterative technique. As an application, an example is presented to enrich the main results of this article.

Download Full-text

Monotone iterative technique for impulsive Riemann-Liouville fractional differential equations

Filomat ◽

10.2298/fil1809381c ◽

2018 ◽

Vol 32 (9) ◽

pp. 3381-3395 ◽

Cited By ~ 3

Author(s):

Renu Chaudhary ◽

Dwijendra Pandey

Keyword(s):

Differential Equation ◽

Differential Equations ◽

Fractional Differential Equations ◽

Existence And Uniqueness ◽

Measure Of Noncompactness ◽

Semigroup Theory ◽

Monotone Iterative Technique ◽

Iterative Technique ◽

Monotone Iterative ◽

Fractional Differential

In this article, Monotone iterative technique coupled with the method of lower and upper solutions is employed to discuss the existence and uniqueness of mild solution to an impulsive Riemann-Liouville fractional differential equation. The results are obtained using the concept of measure of noncompactness, semigroup theory and generalized Gronwall inequality for fractional differential equations. At last, an example is given to illustrate the applications of the main results.

Download Full-text