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Null Controllability of Hilfer Fractional Stochastic Differential Inclusions

Fractal and Fractional, 2022
This paper gives the null controllability for nonlocal stochastic differential inclusion with the Hilfer fractional derivative and Clarke subdifferential.
Hamdy M. Ahmed, Mahmoud M. El-Borai, Wagdy El-Sayed, Alaa Elbadrawi   +3 more
doaj   +4 more sources

Hilfer-Katugampola fractional stochastic differential inclusions with Clarke sub-differential

Heliyon
The objective of this paper is to investigate the existence of mild solutions and optimal controls for a class of stochastic Hilfer-Katugampola fractional differential inclusions (SHKFDIs) with non-instantaneous impulsive (NIIs) that is strengthened by ...
Noorah Mshary, Hamdy M. Ahmed, Ahmed S. Ghanem, A.M. Sayed Ahmed   +3 more
doaj   +4 more sources

On Connections Between Stochastic Differential Inclusions and Set-Valued Stochastic Differential Equations Driven by Semimartingales

Journal of Differential Equations, 2017
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Mariusz Michta
exaly   +4 more sources

Asynchronous stochastic approximation with differential inclusions [PDF]

Stochastic Systems, 2012
The asymptotic pseudo-trajectory approach to stochastic approximation of Benaïm, Hofbauer and Sorin is extended for asynchronous stochastic approximations with a set-valued mean field.
David S. Leslie, Steven Perkins
doaj   +6 more sources

Trajectory Controllability of Clarke Subdifferential-Type Conformable Fractional Stochastic Differential Inclusions with Non-Instantaneous Impulsive Effects and Deviated Arguments

Fractal and Fractional, 2023
In this study, the multivalued fixed point theorem, Clarke subdifferential properties, fractional calculus, and stochastic analysis are used to arrive at the system’s mild solution (1). Furthermore, the mean square moment for the aforementioned system (1)
Dimplekumar Chalishajar, Ramkumar Kasinathan, Ravikumar Kasinathan, Varshini Sandrasekaran   +3 more
doaj   +2 more sources

Stochastic Approximations and Differential Inclusions [PDF]

SIAM Journal on Control and Optimization, 2005
The dynamical systems approach to stochastic approximation is generalized to the case where the mean differential equation is replaced by a differential inclusion. The limit set theorem of Benaïm and Hirsch is extended to this situation. Internally chain transitive sets and attractors are studied in detail for set-valued dynamical systems. Applications
Sylvain Sorin, Michel Benaïm, Josef Hofbauer   +2 more
exaly   +5 more sources

Stochastic Approximations and Differential Inclusions, Part II: Applications [PDF]

Mathematics of Operations Research, 2006
We apply the theoretical results on “stochastic approximations and differential inclusions” developed in Benaïm et al. [M. Benaïm, J. Hofbauer, S. Sorin. 2005. Stochastic approximations and differential inclusions. SIAM J. Control Optim. 44 328–348] to several adaptive processes used in game theory, including classical and generalized approachability ...
Sylvain Sorin, Michel Benaïm, Josef Hofbauer   +2 more
exaly   +6 more sources

The effects of Clarke sub-differential and Poisson jumps on nonlocal controllability of Sobolev-type fractional stochastic differential inclusions

Journal of Inequalities and Applications
This paper explores Sobolev-type Atangana–Baleanu fractional stochastic differential inclusions driven by fractional Brownian motion, incorporating Clarke sub-differentials, Poisson jumps, and nonlocal conditions.
Wael W. Mohammed, Hamdy M. Ahmed, Homan Emadifar, Karim K. Ahmed, A. M. Sayed Ahmed   +4 more
doaj   +2 more sources

Stochastic Approximation With Discontinuous Dynamics, Differential Inclusions, and Applications

Annals of Applied Probability, 2023
This work develops new results for stochastic approximation algorithms. The emphases are on treating algorithms and limits with discontinuities. The main ingredients include the use of differential inclusions, set-valued analysis, and non-smooth analysis, and stochastic differential inclusions. Under broad conditions, it is shown that a suitably scaled
Gang George Yin, Nhu Nguyen
exaly   +3 more sources

Stochastic differential inclusions with Hilfer fractional derivative

Annals of the University of Craiova, Mathematics and Computer Science Series, 2022
In this paper, we study the existence of mild solutions of Hilfer fractional stochastic differential inclusions driven by sub fractional Brownian motion in the cases when the multivalued map is convex and non convex.
Meryem Chaouche, Toufik Guendouzi
semanticscholar   +2 more sources