Stability results for neutral stochastic functional differential equations via fixed point methods

2018 ◽  
Vol 93 (7) ◽  
pp. 1726-1734
Author(s):  
Mimia Benhadri ◽  
Tomás Caraballo ◽  
Halim Zeghdoudi
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Functional Differential Equations ◽  
Stochastic Functional Differential Equations ◽  
Fixed Point Methods ◽  
Functional Differential ◽  
Stability Results ◽  
Stochastic Functional

scholarly journals Ulam-Hyers-Rassias Stability of Stochastic Functional Differential Equations via Fixed Point Methods

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Abdellatif Ben Makhlouf ◽  
Lassaad Mchiri ◽  
Mohamed Rhaima
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Stochastic Systems ◽  
Functional Differential Equations ◽  
Stochastic Functional Differential Equations ◽  
Fixed Point Methods ◽  
Functional Differential ◽  
The Stability ◽  
Rassias Stability ◽  
Stochastic Functional

The Ulam-Hyers-Rassias stability for stochastic systems has been studied by many researchers using the Gronwall-type inequalities, but there is no research paper on the Ulam-Hyers-Rassias stability of stochastic functional differential equations via fixed point methods. The main goal of this paper is to investigate the Ulam-Hyers Stability (HUS) and Ulam-Hyers-Rassias Stability (HURS) of stochastic functional differential equations (SFDEs). Under the fixed point methods and the stochastic analysis techniques, the stability results for SFDE are investigated. We analyze two illustrative examples to show the validity of the results.

scholarly journals Razumikhin-type theorem on time-changed stochastic functional differential equations with Markovian switching

2019 ◽  
Vol 17 (1) ◽  
pp. 689-699 ◽  
Author(s):  
Xiaozhi Zhang ◽  
Chenggui Yuan
Keyword(s):  
Differential Equations ◽  
Exponential Stability ◽  
Type Theorem ◽  
Functional Differential Equations ◽  
Markovian Switching ◽  
Stochastic Functional Differential Equations ◽  
Razumikhin Theorem ◽  
Functional Differential ◽  
Stability Results ◽  
Stochastic Functional

Abstract This work is mainly concerned with the exponential stability of time-changed stochastic functional differential equations with Markovian switching. By expanding the time-changed Itô formula and the Razumikhin theorem, we obtain the exponential stability results for the time-changed stochastic functional differential equations with Markovian switching. What’s more, we get many useful stability results by applying our new results to several important types of functional differential equations. Finally, an example is given to demonstrate the effectiveness of the main results.

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