Existence and stability results for Caputo fractional stochastic differential equations with Lévy noise

Maheswari, P. Uma; Balachandran, K.; Annapoorani, N.

doi:10.2298/fil2005739u

Cited by 18 publications

(6 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Then, following Ref. [17], we have no problem giving the existence and uniqueness result of system (1). Theorem 1.…”

Section: Lemma 1 (Time Scale Change Property) Let the Time Scalementioning

confidence: 96%

A Note on Averaging Principles for Fractional Stochastic Differential Equations

Liu,

Zhang,

Wang

et al. 2024

Fractal Fract

View full text Add to dashboard Cite

Over the past few years, many scholars began to study averaging principles for fractional stochastic differential equations since they can provide an approximate analytical method to reduce such systems. However, in the most previous studies, there is a misunderstanding of the standard form of fractional stochastic differential equations, which consequently causes the wrong estimation of the convergence rate. In this note, we take fractional stochastic differential equations with Lévy noise as an example to clarify these two issues. The corrections herein have no effect on the main proofs except the two points mentioned above. The innovation of this paper lies in three aspects: (i) the standard form of the fractional stochastic differential equations is derived under natural time scale; (ii) it is first proved that the convergence interval and rate are related to the fractional order; and (iii) the presented results contain and improve some well known research achievements.

show abstract

“…Then, following Ref. [17], we have no problem giving the existence and uniqueness result of system (1). Theorem 1.…”

Section: Lemma 1 (Time Scale Change Property) Let the Time Scalementioning

confidence: 96%

A Note on Averaging Principles for Fractional Stochastic Differential Equations

Liu,

Zhang,

Wang

et al. 2024

Fractal Fract

View full text Add to dashboard Cite

show abstract

“…Hence, its significance and necessity cannot be overstated. Numerous reports on SDEs with Lévy noise (see [4][5][6]) have been published. For instance, Balasubramaniam [7] discussed the existence of solutions for FSDEs of Hilfer-type with non-instantaneous impulses excited by mixed Brownian motion and Lévy noise.…”

Section: Introductionmentioning

confidence: 99%

The Averaging Principle for Hilfer Fractional Stochastic Evolution Equations with Lévy Noise

Yang,

Lv,

Wang

2023

Fractal Fract

View full text Add to dashboard Cite

This article focuses on deriving the averaging principle for Hilfer fractional stochastic evolution equations (HFSEEs) driven by Lévy noise. We show that the solutions of the averaged equations converge to the corresponding solutions of the original equations, both in the sense of mean square and of probability. Our results enable us to focus on the averaged system rather than the original, more complex one. Given that the existing literature on the averaging principle for Hilfer fractional stochastic differential equations has been established in finite-dimensional spaces, the novelty here is the derivation of the averaging principle for a class of HFSEEs in Hilbert space. Furthermore, an example is allotted to illustrate the feasibility and utility of our results.

show abstract

“…As for the non-Lipschitz condition, Abouagwa et al [7,8] established the existence theorem for solutions by applying the Carathéodory approximation. Under global Lipshitz conditions, with the aid of Picard iteration method and contradiction method, Moghaddam et al [9] and Umamaheswari et al [10] deduced the existence and uniqueness results. In [11][12][13], the monotone iterative method was used to obtain the existence theorem of mild solutions.…”

Section: Introductionmentioning

confidence: 99%

Novel Results on Finite‐Time Stability of Solutions for Stochastic Ψ‐Hilfer Fractional System

Tian

Luo

2023

Mathematical Problems in Engineering

View full text Add to dashboard Cite

This article studies a new kind of Ψ -Hilfer fractional system driven by m -dimensional Brownian motion. By utilizing the generalized Laplace transform and its inverse, the contraction mapping principle, and the properties of a semigroup, we establish the uniqueness of the solution. In addition, finite-time stability is investigated by means of the properties of norm and inequalities scaling technique. As verification, an example is given to show the deduced conclusions.

show abstract

Existence and stability results for Caputo fractional stochastic differential equations with Lévy noise

Cited by 18 publications

References 29 publications

A Note on Averaging Principles for Fractional Stochastic Differential Equations

A Note on Averaging Principles for Fractional Stochastic Differential Equations

The Averaging Principle for Hilfer Fractional Stochastic Evolution Equations with Lévy Noise

Novel Results on Finite‐Time Stability of Solutions for Stochastic Ψ‐Hilfer Fractional System

Contact Info

Product

Resources

About