<p>In this article, we investigate the existence results for Sobolev type nonlocal Hilfer fractional stochastic differential inclusions with a non-dense domain in Hilbert spaces. The analysis is carried out within the framework of fractional calculus, semigroup theory, and multivalued analysis. By applying Dhage’s fixed point theorem in combination with fractional calculus techniques, we establish sufficient conditions ensuring the existence of mild solutions to the considered system. The introduction of nonlocal conditions provides a more realistic framework, allowing the present state of the system to depend on both the initial data and its past history, thus capturing memory-dependent behavior. The approach adopted here effectively handles the challenges arising from the non-dense domain and the stochastic nature of the inclusion. Finally, an illustrative example involving Hilfer fractional stochastic differential inclusions with a non-dense domain is presented to demonstrate the applicability and effectiveness of the developed theoretical framework.</p>

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Existence results of non-densely defined Sobolev type Hilfer fractional stochastic differential inclusions with nonlocal conditions

  • A. Priyadharshini,
  • V. Vijayakumar

摘要

In this article, we investigate the existence results for Sobolev type nonlocal Hilfer fractional stochastic differential inclusions with a non-dense domain in Hilbert spaces. The analysis is carried out within the framework of fractional calculus, semigroup theory, and multivalued analysis. By applying Dhage’s fixed point theorem in combination with fractional calculus techniques, we establish sufficient conditions ensuring the existence of mild solutions to the considered system. The introduction of nonlocal conditions provides a more realistic framework, allowing the present state of the system to depend on both the initial data and its past history, thus capturing memory-dependent behavior. The approach adopted here effectively handles the challenges arising from the non-dense domain and the stochastic nature of the inclusion. Finally, an illustrative example involving Hilfer fractional stochastic differential inclusions with a non-dense domain is presented to demonstrate the applicability and effectiveness of the developed theoretical framework.