Existence and Stability for Stochastic Impulsive Neutral Partial Differential Equations Driven by Rosenblatt Process with Delay and Poisson Jumps

Ouahra, Mouhamed Ait; Boufoussi, Brahim; Lakhel, El Hassan

doi:10.31390/cosa.11.1.07

Cited by 9 publications

(5 citation statements)

References 20 publications

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“…Rosenblatt properties including self-similarity, stationery increment, and long-range dependence in non-central limit theorem, have so far been analyzed by many researchers ( [11], [13], [14]). Impressive progress of fractional calculus with the stochastic process makes notable improvements in mathematical research.…”

Section: Introductionmentioning

confidence: 99%

Existence and stability behavior of fractional stochastic differential equation driven by Rosenblatt process

C.,

Balasubramaniam

2024

Preprint

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This work focus on a nonlinear mathematical model deal with the stability of visual trajectory track during locomotion in the fish robot is developed. Previously the visual trajectory model has derived through stochastic differential equation. The source of long memory, and more precisely of infinite memory, is due to infinitely large time constants. Thus, Fractional calculus theory is developed to get better model. (1) The fractional stochastic differential equation (FSDEs) is utilized to determine the parameters that ensure the coordination between the unstable visual trajectory track and the stable visual trajectory track of the fish robotic system and robot driver. (2) Existence and stability results are derived through successive approximation and Bihari’s inequality, semigroup theory, and fractional calculus in stochastic settings. (3) Stability results of Rosenblatt process and numerical simulation are established and applied for collision free track in the visual trajectory track of the fish robot. (4) Stability of FSDEs through Rosenblatt process entrusted depletion of collision in the ocean water environment even in tiny particles from the visual trajectory to the fish robot. There is no existing knowledge in this regard. Therefore, the study is conducted. (5) The algorithms have several advantages from gaze shift frame such as terrific quality of randomness, key sensitivity, and collision free location stability. Numerical simulation results manifest the effectiveness, efficiency and feasibility of real-world applications.

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Section: Introductionmentioning

confidence: 99%

Existence and stability behavior of fractional stochastic differential equation driven by Rosenblatt process

C.,

Balasubramaniam

2024

Preprint

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“…In order to make more realistic model, a jump term is included in any dynamical systems. The study of stochastic differential equations driven by Poisson jumps has considerable attentions [9,8,5,10]. Recently, Tamilalagan et al [10] have investigated the stochastic fractional evolution inclusions driven by Poisson jumps in a Hilbert space.…”

Section: Introductionmentioning

confidence: 99%

Fractional neutral stochastic integrodifferential equations with Caputo fractional derivative: Rosenblatt process, Poisson jumps and Optimal control

Ravikumar¹,

Ramkumar²,

Ahmed

2023

Proyecciones (Antofagasta)

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The objective of this paper is to investigate the existence of mild solutions and optimal controls for a class of fractional neutral stochastic integrodifferential equations driven by Rosenblatt process and Poisson jumps in Hilbert spaces. First we establish a new set of sufficient conditions for the existence of mild solutions of the aforementioned fractional systems by using the successive approximation approach. The results are formulated and proved by using the fractional calculus, solution operator and stochastic analysis techniques. The existence of optimal control pairs of system governed by fractional neutral stochastic differential equations driven by Rosenblatt process and poisson jumps is also been presented. An example is provided to illustrate the theory.

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“…In the literature, there are numerous articles that studied various theoretical facets of the Rosenblatt process. Ouahra et al [35] discussed the qualitative properties of an stochastic delayed neutral functional differential system including impulses, Poisson jump, and the Rosenblatt process. Leonenko and Ahn [7] gave a fruitful result for the rate of convergence of the Rosenblatt process.…”

Section: Introductionmentioning

confidence: 99%

Existence of solutions for non-autonomous second-order stochastic inclusions with Clarke’s subdifferential and non instantaneous impulses

Upadhyay

Kumar

2022

Filomat

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This manuscript explores a new class of non-autonomous second-order stochastic inclusions of Clarke?s subdifferential form with non-instantaneous impulses (NIIs), unbounded delay, and the Rosenblatt process in Hilbert spaces. The existence of a solution is deduced by employing a fixed point strategy for a set-valued map together with the evolution operator and stochastic analysis approach. An example is analyzed for theoretical developments.

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Existence and Stability for Stochastic Impulsive Neutral Partial Differential Equations Driven by Rosenblatt Process with Delay and Poisson Jumps

Cited by 9 publications

References 20 publications

Existence and stability behavior of fractional stochastic differential equation driven by Rosenblatt process

Existence and stability behavior of fractional stochastic differential equation driven by Rosenblatt process

Fractional neutral stochastic integrodifferential equations with Caputo fractional derivative: Rosenblatt process, Poisson jumps and Optimal control

Existence of solutions for non-autonomous second-order stochastic inclusions with Clarke’s subdifferential and non instantaneous impulses

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