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Integral inequality approach to existence and approximate controllability of higher-order Hilfer fractional stochastic inclusions with impulses and jumps

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The aim is to analyze the existence and approximate controllability of higher-order Hilfer fractional stochastic inclusions incorporating various complexities.
Analytical investigation of higher-order stochastic inclusions
Use of Brownian motion and Poisson jump perturbations
Application of Hilfer-type fractional integral inequalities
Fixed point principles for multi-valued mappings
Construction of examples to validate theoretical findings
Existence conditions for mild solutions were established
Approximate controllability was demonstrated under impulsive effects and jumps
New integral inequality estimates were derived for the stochastic system
The approach effectively handles nonlocal initial conditions and hereditary memory terms
Constructive examples confirmed the applicability of the theoretical results

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Analytical investigation of stochastic inclusions reveals existence and controllability conditions under impulses and jumps.

Ahmed et al. (2026) studied this question.

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