Om Prakash Kumar Sharma, Ramesh Kumar Vats, Ankit Kumar

New exploration on approximate controllability of fractional neutral‐type delay stochastic differential inclusions with non‐instantaneous impulse

  • General Engineering
  • General Mathematics

This paper aims to derive a new set of sufficient conditions for the existence and approximate controllability of neutral‐type fractional stochastic integrodifferential inclusions with infinite delay and non‐instantaneous impulse in a separable Hilbert space using the Atangana–Baleanu Caputo fractional derivative. We investigate the existence of a mild solution for the Atangana–Baleanu Caputo fractional neutral‐type delay integrodifferential stochastic system while taking into account the non‐instantaneous impulses. For this purpose, the Atangana–Baleanu Caputo fractional neutral‐type impulsive delay stochastic system is transferred into an equivalent fixed point problem via an integral operator, and then, the Bohnenblust–Karlin fixed point approach is applied. Further, the approximate controllability results of the proposed nonlinear stochastic impulsive control system are established under the consideration that the corresponding linear system is approximately controllable. The set of sufficient conditions is established by using the concepts of stochastic analysis, fractional calculus, fixed point technique, semigroup theory of bounded linear operators, and the theory of multivalued maps. To illustrate the abstract results, we provide an example at the end of the paper.

Need a simple solution for managing your BibTeX entries? Explore CiteDrive!

  • Web-based, modern reference management
  • Collaborate and share with fellow researchers
  • Integration with Overleaf
  • Comprehensive BibTeX/BibLaTeX support
  • Save articles and websites directly from your browser
  • Search for new articles from a database of tens of millions of references
Try out CiteDrive

More from our Archive