Optimal control of Sobolev-type stochastic Hilfer fractional non-instantaneous impulsive differential inclusion involving Poisson jumps and Clarke subdifferential

• Published in: IET control theory & applications Vol. 14; no. 6; pp. 887 - 899
• Main Authors: Durga, N, Muthukumar, P
• Format: Journal Article
• Language: English
• Published: The Institution of Engineering and Technology 16.04.2020
• Subjects: Balder theorem; Clarke subdifferential; differential equations; Leray‐Schauder type fixed point theorem; noninstantaneous impulses; optimal control; Poisson jumps; Research Article; Sobolev‐type stochastic Hilfer fractional noninstantaneous impulsive differential inclusion; stochastic analysis; stochastic dam pollution model; stochastic processes; Balder theorem; Clarke subdifferential; noninstantaneous impulses; Poisson jumps; optimal control; Sobolev-type stochastic Hilfer fractional noninstantaneous impulsive differential inclusion; stochastic processes; Leray-Schauder type fixed point theorem; stochastic dam pollution model; stochastic analysis; differential equations
• ISSN: 1751-8644; 1751-8652; 1751-8652
• DOI: 10.1049/iet-cta.2019.0167

This article is concerned with the optimal control of Sobolev-type Hilfer fractional non-instantaneous impulsive differential inclusion driven by Poisson jumps and Clarke subdifferential. Initially, the existence of a mild solution is established for the proposed Hilfer type fractional problem with novel ideas of non-instantaneous impulses. The non-linear alternative of Leray-Schauder type fixed point theorem, stochastic analysis, the measure of non-compactness and the multivalued analysis are applied to prove the mild solution. Further, the existence of optimal control is derived by employing Balder's theorem. Finally, the application as a stochastic dam pollution model is provided to illustrate the developed theoretical results.