Trajectory controllability of Hilfer fractional neutral stochastic differential equation with deviated argument and mixed fractional Brownian motion

This manuscript is concerned with the trajectory controllability of Hilfer fractional neutral stochastic differential equation having deviated arguments and mixed fractional Brownian motion with the Hurst parameter . The proposed Hilfer fractional system's solvability in Hilbert space is acquir...

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Bibliographic Details
Published inOptimization Vol. 72; no. 11; pp. 2865 - 2891
Main Authors Durga, N., Muthukumar, P., Malik, Muslim
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 02.11.2023
Taylor & Francis LLC
Subjects
Brownian motion
Controllability
Deviated argument
Differential equations
Fixed points (mathematics)
fractional Brownian motion
Fractional calculus
Hilbert space
Hilfer fractional derivative
neutral stochastic differential equation with infinite delay
Trajectory control
Trajectory controllability
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Summary:This manuscript is concerned with the trajectory controllability of Hilfer fractional neutral stochastic differential equation having deviated arguments and mixed fractional Brownian motion with the Hurst parameter . The proposed Hilfer fractional system's solvability in Hilbert space is acquired by employing fractional calculus, stochastic analysis, semigroup theory, and Krasnoselskii's fixed point theorem. Furthermore, under some suitable assumptions, the considered system's trajectory controllability is established using generalized Gronwall's inequality. Finally, an example is delivered to illustrate the obtained theoretical results.
ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2022.2080551