What question did this study set out to answer?

This research aims to find conditions for the existence of a solution and controllability in a nonlinear stochastic system involving fractional calculus.

June 12, 2026International Journal of Systems Science

New qualitative study on fractional Sobolev-type delayed stochastic multivalued system with extended impulsive dynamics: existence and controllability

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Authors

OSO. P. SharmaJagannath University RVRamesh Kumar VatsNational Institute of Technology Hamirpur

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Qualitative study investigates existence and controllability in complex stochastic systems, indicating promising modeling advancements.

Key Points

This research aims to find conditions for the existence of a solution and controllability in a nonlinear stochastic system involving fractional calculus.
Studied a fractional Sobolev-type delayed stochastic multivalued system in a separable Hilbert space.
Transformed the control problem into a fixed point problem using the Ψ-Riemann-Liouville fractional integral operator.
Applied the Karlin fixed point theorem to establish the existence of a mild solution.
Established sufficient conditions for the existence of integral-form mild solutions in the proposed system.
Verified approximate controllability given the linear system is already approximately controllable.

Cite This Study

Sharma et al. (2026) studied this question.

synapsesocial.com/papers/6a2ba2c18101cf8926f01a28 https://doi.org/10.1080/00207721.2026.2680467

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New qualitative study on fractional Sobolev-type delayed stochastic multivalued system with extended impulsive dynamics: existence and controllability

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Cite This Study

New qualitative study on fractional Sobolev-type delayed stochastic multivalued system with extended impulsive dynamics: existence and controllability

Discussion

Member takes

Implication

Key Points

Cite This Study

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