Existence results for the system of partial differential inclusions with uncertainty

Article type: Research Article

Authors: Rashid, Maliha^a | Mehmood, Nayyar^{a; b; *} | Shaheen, Sumbal^a

Affiliations: [a] Department of Mathematics and Statistics, International Islamic University, H-10, Islamabad, Pakistan | [b] Department of Mathematical Sciences, College of Science, UAE University, Al Ain, UAE

Correspondence: [*] Corresponding author. Nayyar Mehmood. E-mail: nayyarmaths@gmail.com.

Abstract: It is well known while dealing with uncertainty, fuzzy sets are assumed to be more efficient than ordinary. In this article, the existence results for a certain types of the system of fuzzy differential inclusions with integral types of local conditions have been obtained. Two systems of fuzzy differential inclusions are considered, the existence result for first system is obtained by using a well-known topological fixed point result, while for the other, a multivalued fixed point result is used. This study has generalized many results present in the literature. To validate the study, non-trivial examples are provided.

Keywords: Fuzzy partial differential inclusions, solutions, existence results

DOI: 10.3233/JIFS-18332

Journal: Journal of Intelligent & Fuzzy Systems, vol. 35, no. 2, pp. 2547-2557, 2018