scholarly journals Existence and uniqueness of extremal mild solutions for non-autonomous nonlocal integro-differential equations via monotone iterative technique

Filomat ◽  
2019 ◽  
Vol 33 (10) ◽  
pp. 2985-2993 ◽  
Author(s):  
Arshi Meraj ◽  
Dwijendra Pandey
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Measure Of Noncompactness ◽  
Nonlocal Condition ◽  
Mild Solutions ◽  
Upper And Lower Solutions ◽  
Monotone Iterative Method ◽  
Evolution System ◽  
Ordered Banach Space ◽  
Monotone Iterative

In this work, we will discuss the existence and uniqueness of extremal mild solutions for non-autonomous integro-differential equations having nonlocal condition via monotone iterative method with upper and lower solutions in an ordered Banach space X, using evolution system and measure of noncompactness.

scholarly journals Monotone iterative technique for non-autonomous semilinear differential equations with nonlocal condition

2019 ◽  
Vol 52 (1) ◽  
pp. 29-39 ◽  
Author(s):  
Arshi Meraj ◽  
Dwijendra Narain Pandey
Keyword(s):  
Differential Equations ◽  
Measure Of Noncompactness ◽  
Nonlocal Condition ◽  
Mild Solutions ◽  
Upper And Lower Solutions ◽  
Monotone Iterative Technique ◽  
Monotone Iterative Method ◽  
Evolution System ◽  
Monotone Iterative ◽  
Norm Space

AbstractThe objective of this article is to discuss the existence and uniqueness of mild solutions for a class of non-autonomous semilinear differential equations with nonlocal condition via monotone iterative method with upper and lower solutions in an ordered complete norm space X, using evolution system and measure of noncompactness.

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.

scholarly journals Existence of positive S-asymptotically periodic solutions of the fractional evolution equations in ordered Banach spaces

2021 ◽  
Vol 26 (5) ◽  
pp. 928-946
Author(s):  
Qiang Li ◽  
Lishan Liu ◽  
Mei Wei
Keyword(s):  
Evolution Equations ◽  
Mild Solutions ◽  
Upper And Lower Solutions ◽  
Periodic Problem ◽  
Growth Conditions ◽  
Monotone Iterative Method ◽  
Monotone Iterative ◽  
Asymptotically Periodic ◽  
Asymptotically Periodic Solutions ◽  
Ordered Banach Spaces

In this paper, we discuss the asymptotically periodic problem for the abstract fractional evolution equation under order conditions and growth conditions. Without assuming the existence of upper and lower solutions, some new results on the existence of the positive S-asymptotically ω-periodic mild solutions are obtained by using monotone iterative method and fixed point theorem. It is worth noting that Lipschitz condition is no longer needed, which makes our results more widely applicable.

Monotone iterative technique for impulsive Riemann-Liouville fractional differential equations

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3381-3395 ◽  
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.

scholarly journals Monotone-Iterative Method for the Initial Value Problem with Initial Time Difference for Differential Equations with “Maxima”

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
S. Hristova ◽  
A. Golev
Keyword(s):  
Differential Equations ◽  
Initial Value Problem ◽  
Upper And Lower Solutions ◽  
Successive Approximations ◽  
Initial Time ◽  
Time Interval ◽  
Monotone Iterative Method ◽  
Initial Value ◽  
Monotone Iterative ◽  
The Given

The object of investigation of the paper is a special type of functional differential equations containing the maximum value of the unknown function over a past time interval. An improved algorithm of the monotone-iterative technique is suggested to nonlinear differential equations with “maxima.” The case when upper and lower solutions of the given problem are known at different initial time is studied. Additionally, all initial value problems for successive approximations have both initial time and initial functions different. It allows us to construct sequences of successive approximations as well as sequences of initial functions, which are convergent to the solution and to the initial function of the given initial value problem, respectively. The suggested algorithm is realized as a computer program, and it is applied to several examples, illustrating the advantages of the suggested scheme.

A MONOTONE-ITERATIVE METHOD FOR FINDING PERIODIC SOLUTION OF AN IMPULSIVE DIFFERENTIAL EQUATIONS AND APPLICATION

2008 ◽  
Vol 01 (02) ◽  
pp. 247-256
Author(s):  
JIAWEI DOU
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Upper And Lower Solutions ◽  
Impulsive Differential Equations ◽  
Iteration Process ◽  
Impulsive System ◽  
Monotone Iterative Method ◽  
Initial Value ◽  
Monotone Iterative ◽  
Monotone Iterations

In this paper, using the method of upper and lower solutions and its associated monotone iterations, we establish a new monotone-iterative scheme for finding periodic solutions of an impulsive differential equations. This method leads to the existence of maximal and minimal periodic solutions which can be computed from a linear iteration process in the same fashion as for impulsive differential equations initial value problem. This method is constructive and can be used to develop a computational algorithm for numerical solution of the periodic impulsive system. Our existence result improves a result established in [1]. The result is applied to a model of mutualism of Lotka–Volterra type which involves interactions among a mutualist-competitor, a competitor and a mutualist, the existence of positive periodic solutions of the model is obtained.

scholarly journals Periodic Boundary Value Problems for Semilinear Fractional Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Jia Mu ◽  
Yongxiang Li
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Periodic Boundary ◽  
Mild Solutions ◽  
Boundary Value ◽  
Upper And Lower Solutions ◽  
Parabolic Partial Differential Equations ◽  
Monotone Iterative ◽  
Periodic Boundary Value Problems ◽  
Fractional Differential

We study the periodic boundary value problem for semilinear fractional differential equations in an ordered Banach space. The method of upper and lower solutions is then extended. The results on the existence of minimal and maximal mild solutions are obtained by using the characteristics of positive operators semigroup and the monotone iterative scheme. The results are illustrated by means of a fractional parabolic partial differential equations.

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.

On fractional differential equations with state-dependent delay via Kuratowski measure of noncompactness

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 451-460 ◽  
Author(s):  
Mohammed Belmekki ◽  
Kheira Mekhalfi
Keyword(s):  
Differential Equations ◽  
Measure Of Noncompactness ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Kuratowski Measure Of Noncompactness ◽  
State Dependent ◽  
State Dependent Delay ◽  
Liouville Fractional Derivative ◽  
Fractional Differential ◽  
Functional Differential

This paper is devoted to study the existence of mild solutions for semilinear functional differential equations with state-dependent delay involving the Riemann-Liouville fractional derivative in a Banach space and resolvent operator. The arguments are based upon M?nch?s fixed point theoremand the technique of measure of noncompactness.

Existence results of mild solutions for impulsive fractional integro-differential evolution equations with infinite delay

2014 ◽  
Vol 17 (4) ◽  
Author(s):  
Shengli Xie
Keyword(s):  
Differential Equations ◽  
Differential Evolution ◽  
Existence Theorem ◽  
Banach Spaces ◽  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Infinite Delay ◽  
Mild Solutions ◽  
Existence Results ◽  
Order Case

AbstractIn this paper we prove the existence and uniqueness of mild solutions for impulsive fractional integro-differential evolution equations with infinite delay in Banach spaces. We generalize the existence theorem for integer order differential equations to the fractional order case. The results obtained here improve and generalize many known results.

Sign in / Sign up

Export Citation Format

Share Document