scholarly journals The Existence of extremal solutions to nonlinear fractional integro-differential equations with advanced arguments

2016 ◽  
Vol 5 (45) ◽  
Author(s):  
Neda Khodabakhshi
Keyword(s):  
Differential Equations ◽  
Extremal Solutions

Existence of Extremal Solutions for Impulsive Delay Fuzzy Differential Equations in n-Dimensional Fuzzy Vector Space

2012 ◽  
Vol 542-543 ◽  
pp. 188-193
Author(s):  
Young Chel Kwun ◽  
Hae Eun Youm ◽  
Ja Hong Koo ◽  
Jin Han Park ◽  
Jong Jin Seo
Keyword(s):  
Differential Equations ◽  
Vector Space ◽  
Delay Condition ◽  
Extremal Solutions ◽  
Impulsive Delay ◽  
Equations With Delay ◽  
Fuzzy Vector

In this paper, we study the existence of extremal solutions for impulsive delay fuzzy differential equations in n-dimensional fuzzy vector space. This is an extension of the result of Kwun et al. [2] to impulsive fuzzy differential equations with delay condition.

RESULTS FOR SIXTH ORDER POSITIVELY HOMOGENEOUS EQUATIONS

2009 ◽  
Vol 14 (1) ◽  
pp. 25-32 ◽  
Author(s):  
Tatjana Garbuza
Keyword(s):  
Differential Equations ◽  
Linear Equations ◽  
Sixth Order ◽  
Extremal Solutions ◽  
Conjugate Points ◽  
Comparison Results

We consider positively homogeneous the sixth order differential equations of the type x (6) = h(t, x), where hpossesses the property that h(t, cx) = ch(t, x) for c ≥ 0. This class includes the linear equations x (6) = p(t)x and piece‐wise linear ones x (6) = k 2 x+ - k 1 x− . We consider conjugate points and angles associated with extremal solutions and prove some comparison results.

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.

Existence of extremal solutions for interval-valued functional integro-differential equations

2016 ◽  
Vol 30 (6) ◽  
pp. 3495-3512 ◽  
Author(s):  
Le Thanh Quang ◽  
Ngo Van Hoa ◽  
Nguyen Dinh Phu ◽  
Tran Thanh Tung
Keyword(s):  
Differential Equations ◽  
Extremal Solutions ◽  
Interval Valued

scholarly journals Monotone Iterative Technique for Conformable Fractional Differential Equations with Deviating Arguments

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.

Extremal solutions of Cauchy problems for abstract fractional differential equations

2013 ◽  
Vol 63 (4) ◽  
Author(s):  
JinRong Wang ◽  
Yong Zhou ◽  
Milan Medveď
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Singular Integral ◽  
Fractional Differential Equations ◽  
Existence Results ◽  
Extremal Solutions ◽  
Cauchy Problems ◽  
Hybrid Fixed Point Theorem ◽  
Fractional Differential

AbstractIn this paper, we study the extremal solutions of Cauchy problems for abstract fractional differential equations. Some definitions such as L 1-Lipschitz-like, L 1-Carathéodory-like and L 1-Chandrabhan-like are introduced. By virtue of the singular integral inequalities with several nonlinearities due to Medved’, the properties of solutions are given. By using a hybrid fixed point theorem due to Dhage, existence results for extremal solutions are established. Finally, we present an example to illustrate our main results.

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