scholarly journals Qualitative properties of solutions of fractional differential and difference equations arising in physical models

Fractals ◽  
2021 ◽  
Author(s):  
Zareen A. Khan ◽  
Hijaz Ahmad
Keyword(s):  
Difference Equations ◽  
Physical Models ◽  
Qualitative Properties ◽  
Fractional Differential ◽  
Qualitative Properties Of Solutions

scholarly journals OSCILLATION AND COMPARISON THEOREMS FOR NEUTRAL DIFFERENCE EQUATIONS

1994 ◽  
Vol 25 (4) ◽  
pp. 343-352
Author(s):  
B. G. ZHANG ◽  
PENGXIANG YAN
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Comparison Theorems ◽  
Qualitative Properties ◽  
Neutral Difference Equation ◽  
Neutral Difference Equations ◽  
Riccati Techniques ◽  
Qualitative Properties Of Solutions

In this paper we study qualitative properties of solutions of the neutral difference equation $$ \Delta(y_n-py_{n-k})+\sum_{i=1}^m q_n^i y_{n-k_i} =0 $$ $$ y_n=A_n \quad \text{ for } n=-M, \cdots, -1, 0$$ where $p \ge 1$, $M =\max\{k, k_1, \cdots, k_m\}$, and $k$, $k_i$, $i =1, \cdots, m$, are nonnegative integers. Riccati techniques are used.  

scholarly journals Qualitative Analyses of Integro-Fractional Differential Equations with Caputo Derivatives and Retardations via the Lyapunov–Razumikhin Method

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 58
Author(s):  
Osman Tunç ◽  
Özkan Atan ◽  
Cemil Tunç ◽  
Jen-Chih Yao
Keyword(s):  
Asymptotic Stability ◽  
Lyapunov Function ◽  
Differential Equations ◽  
Fractional Derivatives ◽  
Qualitative Properties ◽  
Caputo Fractional Derivatives ◽  
Fractional Differential ◽  
Weaker Conditions ◽  
Qualitative Properties Of Solutions ◽  
Qualitative Analyses

The purpose of this paper is to investigate some qualitative properties of solutions of nonlinear fractional retarded Volterra integro-differential equations (FrRIDEs) with Caputo fractional derivatives. These properties include uniform stability, asymptotic stability, Mittag–Leffer stability and boundedness. The presented results are proved by defining an appropriate Lyapunov function and applying the Lyapunov–Razumikhin method (LRM). Hence, some results that are available in the literature are improved for the FrRIDEs and obtained under weaker conditions via the advantage of the LRM. In order to illustrate the results, two examples are provided.

Qualitative properties of solutions to set optimization problems

2021 ◽  
Vol 40 (2) ◽  
Author(s):  
Lam Quoc Anh ◽  
Nguyen Huu Danh ◽  
Pham Thanh Duoc ◽  
Tran Ngoc Tam
Keyword(s):  
Optimization Problems ◽  
Set Optimization ◽  
Qualitative Properties ◽  
Qualitative Properties Of Solutions

Old and New Results for First Order Periodic ODEs without Uniqueness: a Comprehensive Study by Lower and Upper Solutions

2004 ◽  
Vol 4 (3) ◽  
Author(s):  
Franco Obersnel ◽  
Pierpaolo Omari
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Lower And Upper Solutions ◽  
Elementary Approach ◽  
Qualitative Properties ◽  
First Order ◽  
The Past ◽  
The Cauchy Problem ◽  
Qualitative Properties Of Solutions ◽  
Comprehensive Study

AbstractAn elementary approach, based on a systematic use of lower and upper solutions, is employed to detect the qualitative properties of solutions of first order scalar periodic ordinary differential equations. This study is carried out in the Carathéodory setting, avoiding any uniqueness assumption, in the future or in the past, for the Cauchy problem. Various classical and recent results are recovered and generalized.

scholarly journals Radially symmetric solutions to the Hénon–Lane–Emden system on the critical hyperbola

2014 ◽  
Vol 16 (03) ◽  
pp. 1350030 ◽  
Author(s):  
Roberta Musina ◽  
K. Sreenadh
Keyword(s):  
Variational Methods ◽  
Existence Results ◽  
Qualitative Properties ◽  
Radially Symmetric Solutions ◽  
Qualitative Properties Of Solutions

We use variational methods to study the existence of non-trivial and radially symmetric solutions to the Hénon–Lane–Emden system with weights, when the exponents involved lie on the "critical hyperbola". We also discuss qualitative properties of solutions and non-existence results.

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