Existence and Uniqueness of Mild Solution for Fractional-Order Controlled Fuzzy Evolution Equation. (20th December 2021)

• Record Type: Journal Article
• Authors: Iqbal, Naveed; Niazi, Azmat Ullah Khan; Shafqat, Ramsha; Zaland, Shamsullah
• Other Names: Gulzar Muhammad Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2021(2021)
• Publication Date: 2021-12-20
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2021/5795065
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : In this article, we investigated the existence and uniqueness of mild solutions for fractional-order controlled fuzzy evolution equations with Caputo derivatives of the controlled fuzzy nonlinear evolution equation of the form 0 c D I γ x I = α x I + P I, x I + A I W I, I ∈ 0, T, x I 0 = x 0, in which γ ∈ 0, 1, E 1 is the fuzzy metric space and I = 0, T is a real line interval. With the help of few conditions on functions P : I × E 1 × E 1 ⟶ E 1, W I is control and it belongs to E 1, A ∈ F I, L E 1, and α stands for the highly continuous fuzzy differential equation generator. Finally, a few instances of fuzzy fractional differential equations are shown.