Discussion on Existence of Mild Solutions for Hilfer Fractional Neutral Stochastic Evolution Equations Via Almost Sectorial Operators with Delay

Sivasankar, Sivajiganesan; Udhayakumar, R.

doi:10.1007/s12346-023-00773-4

Cited by 11 publications

(4 citation statements)

References 37 publications

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“…Additionally, refs. [14,15] proved the existence of mild solutions for a class of stochastic evolution equations with Hilfer fractional derivatives H D µ,ν 0 + , where µ ∈ (0, 1), ν ∈ [0, 1].…”

Section: Introductionmentioning

confidence: 99%

The Existence of Mild Solutions for Hilfer Fractional Stochastic Evolution Equations with Order μ∈(1,2)

Zhou

2023

Fractal Fract

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In this study, we investigate the existence of mild solutions for a class of Hilfer fractional stochastic evolution equations with order μ∈(1,2) and type ν∈[0,1]. We prove the existence of mild solutions of Hilfer fractional stochastic evolution equations when the semigroup is compact as well as noncompact. Our approach is based on the Schauder fixed point theorem, the Ascoli–Arzelà theorem and the Kuratowski measure of noncompactness. An example is also provided, to demonstrate the efficacy of this method.

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Section: Introductionmentioning

confidence: 99%

The Existence of Mild Solutions for Hilfer Fractional Stochastic Evolution Equations with Order μ∈(1,2)

Zhou

2023

Fractal Fract

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“…SFDEs combine both of these concepts by considering a stochastic process whose evolution is described by a fractional differential equation. These equations have been used to model many complex phenomena, including turbulence, anomalous diffusion, and financial markets [4][5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Khasminskii Approach for $$\psi $$-Caputo Fractional Stochastic Pantograph Problem

Alqudah,

Boulares,

Abdalla

et al. 2024

Qual. Theory Dyn. Syst.

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In this manuscript, we study an averaging principle for fractional stochastic pantograph differential equations (FSDPEs) in the $$\psi $$ ψ -sense accompanied by Brownian movement. Under certain assumptions, we are able to approximate solutions for FSPEs by solutions to averaged stochastic systems in the sense of mean square. Analysis of system solutions before and after the average allows extending the classical Khasminskii approach to random fractional differential equations in the sense of $$\psi $$ ψ -Caputo. For clarity, we present at the end an applied example to facilitate the clarification of the theoretical results obtained

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“…Hilfer [11] introduced a fractional derivative, which is a generalization of both R-L and the Caputo fractional derivatives, known as the Hilfer fractional derivative (HFD). Some authors [12][13][14][15][16] examined the existence of mild solution results of FDEs by utilizing HFD. Recently, the researcher in [17] investigated the HF neutral stochastic differential equations (SDEs) with NII by employing the Mönch fixed-point method.…”

Section: Introductionmentioning

confidence: 99%

New Study on the Controllability of Non-Instantaneous Impulsive Hilfer Fractional Neutral Stochastic Evolution Equations with Non-Dense Domain

Gokul,

Almarri,

Sivasankar

et al. 2024

Fractal Fract

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The purpose of this work is to investigate the controllability of non-instantaneous impulsive (NII) Hilfer fractional (HF) neutral stochastic evolution equations with a non-dense domain. We construct a new set of adequate assumptions for the existence of mild solutions using fractional calculus, semigroup theory, stochastic analysis, and the fixed point theorem. Then, the discussion is driven by some suitable assumptions, including the Hille–Yosida condition without the compactness of the semigroup of the linear part. Finally, we provide examples to illustrate our main result.

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Discussion on Existence of Mild Solutions for Hilfer Fractional Neutral Stochastic Evolution Equations Via Almost Sectorial Operators with Delay

Cited by 11 publications

References 37 publications

The Existence of Mild Solutions for Hilfer Fractional Stochastic Evolution Equations with Order μ∈(1,2)

The Existence of Mild Solutions for Hilfer Fractional Stochastic Evolution Equations with Order μ∈(1,2)

Khasminskii Approach for $$\psi $$-Caputo Fractional Stochastic Pantograph Problem

New Study on the Controllability of Non-Instantaneous Impulsive Hilfer Fractional Neutral Stochastic Evolution Equations with Non-Dense Domain

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