scholarly journals ULAM TYPE STABILITY RESULTS FOR NON-INSTANTANEOUS IMPULSIVE DIFFERENTIAL EQUATIONS WITH FINITE STATE DEPENDENT DELAY

2018 ◽  
Vol 28 (1) ◽  
Author(s):  
RAVI AGARWAL ◽  
SNEZHANA SHRISTOVA ◽  
DONAL O'REGAN
Keyword(s):  
Differential Equations ◽  
Impulsive Differential Equations ◽  
State Dependent ◽  
State Dependent Delay ◽  
Finite State ◽  
Ulam Type Stability ◽  
Stability Results

Ulam type stability for non-instantaneous impulsive Caputo fractional differential equations with finite state dependent delay

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ravi Agarwal ◽  
Snezhana Hristova ◽  
Donal O’Regan
Keyword(s):  
Lower Bound ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Sufficient Conditions ◽  
State Dependent ◽  
State Dependent Delay ◽  
Caputo Fractional Differential Equations ◽  
Finite State ◽  
Fractional Differential ◽  
Ulam Type Stability

AbstractFour Ulam type stability concepts for non-instantaneous impulsive fractional differential equations with state dependent delay are introduced. Two different approaches to the interpretation of solutions are investigated. We study the case of an unchangeable lower bound of the Caputo fractional derivative and the case of a lower bound coinciding with the point of jump for the solution. In both cases we obtain sufficient conditions for Ulam type stability. An example is also provided to illustrate both approaches.

Stability results for fractional differential equations with state-dependent delay and not instantaneous impulses

2017 ◽  
Vol 67 (4) ◽  
Author(s):  
Saïd Abbas ◽  
Mouffak Benchohra
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Darboux Problem ◽  
State Dependent ◽  
State Dependent Delay ◽  
Fractional Differential ◽  
Functional Differential ◽  
Ulam’S Type Stability ◽  
Stability Results ◽  
Stability Concepts

AbstractIn this paper, we shall present some uniqueness and Ulam’s type stability concepts for the Darboux problem of partial functional differential equations with not instantaneous impulses and state-dependent delay in Banach spaces. Some examples are also provided to illustrate our results.

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.

Sign in / Sign up

Export Citation Format

Share Document