Non-Instantaneous Impulsive Fractional Neutral Differential Equations with State-Dependent Delay

2017 ◽  
Vol 3 (3) ◽  
pp. 207-218 ◽  
Author(s):  
Annamalai Anguraj ◽  
Subramaniam Kanjanadevi
Keyword(s):  
Differential Equations ◽  
Neutral Differential Equations ◽  
State Dependent ◽  
State Dependent Delay

A New Investigation on Fractional-Ordered Neutral Differential Systems with State-Dependent Delay

2019 ◽  
Vol 20 (7-8) ◽  
pp. 803-809 ◽  
Author(s):  
N. Valliammal ◽  
C. Ravichandran ◽  
Zakia Hammouch ◽  
Haci Mehmet Baskonus
Keyword(s):  
Differential Equations ◽  
Mild Solutions ◽  
Existence Results ◽  
Differential Systems ◽  
Neutral Differential Equations ◽  
State Dependent ◽  
State Dependent Delay ◽  
Fractional Differential ◽  
Noncompact Measure ◽  
Equations With Delay

AbstractFractional differential equations with delay behaviors occur in fields like physical and biological ones with state-dependent delay or nonconstant delay and has drawn the attention of researchers. The main goal of the present work is to study the existence of mild solutions of neutral differential system along state-dependent delay in Banach space. By employing the fractional theory, noncompact measure and Mönch’s theorem, we investigate the existence results for neutral differential equations of fractional order with state-dependent delay. An illustration of derived results is offered.

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.

NUMERICAL BIFURCATION ANALYSIS OF DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY

2001 ◽  
Vol 11 (03) ◽  
pp. 737-753 ◽  
Author(s):  
TATYANA LUZYANINA ◽  
KOEN ENGELBORGHS ◽  
DIRK ROOSE
Keyword(s):  
Differential Equations ◽  
Bifurcation Analysis ◽  
Delay Differential Equations ◽  
Constant Delay ◽  
State Dependent ◽  
State Dependent Delay ◽  
Numerical Bifurcation ◽  
Delay Differential ◽  
Steady State Solutions ◽  
Numerical Bifurcation Analysis

In this paper we apply existing numerical methods for bifurcation analysis of delay differential equations with constant delay to equations with state-dependent delay. In particular, we study the computation, continuation and stability analysis of steady state solutions and periodic solutions. We collect the relevant theory and describe open theoretical problems in the context of bifurcation analysis. We present computational results for two examples and compare with analytical results whenever possible.

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