Approximate Controllability via Resolvent Operators of Sobolev-Type Fractional Stochastic Integrodifferential Equations with Fractional Brownian Motion and Poisson Jumps

2018 ◽  
Vol 45 (4) ◽  
pp. 1045-1059 ◽  
Author(s):  
Hamdy M. Ahmed
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Approximate Controllability ◽  
Integrodifferential Equations ◽  
Sobolev Type ◽  
Resolvent Operators ◽  
Poisson Jumps

Noninstantaneous impulsive and nonlocal Hilfer fractional stochastic integrodifferential equations with fractional Brownian motion and Poisson jumps

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Hamdy M. Ahmed ◽  
Mahmoud M. El-Borai ◽  
Mohamed E. Ramadan
Keyword(s):  
Fixed Point ◽  
Brownian Motion ◽  
Fixed Point Theorem ◽  
Fractional Calculus ◽  
Fractional Brownian Motion ◽  
Mild Solution ◽  
Stochastic Analysis ◽  
Integrodifferential Equations ◽  
Poisson Jumps ◽  
New Class

AbstractIn this paper, we introduce the mild solution for a new class of noninstantaneous and nonlocal impulsive Hilfer fractional stochastic integrodifferential equations with fractional Brownian motion and Poisson jumps. The existence of the mild solution is derived for the considered system by using fractional calculus, stochastic analysis and Sadovskii’s fixed point theorem. Finally, an example is also given to show the applicability of our obtained theory.

Global attracting sets of neutral stochastic functional integro-differential equations driven by a fractional Brownian motion

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
A. Bakka ◽  
S. Hajji ◽  
D. Kiouach
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Brownian Motion ◽  
Differential Equations ◽  
Fractional Brownian Motion ◽  
Sufficient Conditions ◽  
Integrodifferential Equations ◽  
Hurst Parameter ◽  
Fixed Point Principle ◽  
Stochastic Functional

Abstract By means of the Banach fixed point principle, we establish some sufficient conditions ensuring the existence of the global attracting sets of neutral stochastic functional integrodifferential equations with finite delay driven by a fractional Brownian motion (fBm) with Hurst parameter H ∈ ( 1 2 , 1 ) {H\in(\frac{1}{2},1)} in a Hilbert space.

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