What question did this study set out to answer?

The central aim is to explore the existence and approximate controllability of Sobolev-type fractional stochastic differential equations with infinite delay.

March 22, 2026Fractal and FractionalOpen Access

Approximate Controllability and Existence Results of the Sobolev-Type Fractional Stochastic Differential Equation Driven by a Fractional Brownian Motion

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Authors

SHSaddam HussainUniversity of Malakand MSMuhammad SarwarPrince Sultan University SSSyed Khayyam ShahMiddle East Technical University

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This article investigates approximate controllability in Sobolev-type fractional stochastic systems, suggesting new existence results.

Key Points

The central aim is to explore the existence and approximate controllability of Sobolev-type fractional stochastic differential equations with infinite delay.
Utilized fractional calculus and semigroup theory in an abstract Hilbert space framework.
Employed the Banach contraction principle alongside compactness arguments.
Derived sufficient conditions for approximate controllability using operator-theoretic methods and stochastic analysis.
Established the existence of mild solutions for the fractional stochastic system.
Developed new controllability results extending existing literature on deterministic systems and lower order fractional equations.

Cite This Study

Hussain et al. (2026) studied this question.

synapsesocial.com/papers/69bf89a9f665edcd009e98b6 https://doi.org/10.3390/fractalfract10030203

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Approximate Controllability and Existence Results of the Sobolev-Type Fractional Stochastic Differential Equation Driven by a Fractional Brownian Motion

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Key Points

Cite This Study

Approximate Controllability and Existence Results of the Sobolev-Type Fractional Stochastic Differential Equation Driven by a Fractional Brownian Motion

Discussion

Member takes

Implication

Key Points

Cite This Study

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