Local and Global Existence and Uniqueness of Solution for Class of Fuzzy Fractional Functional Evolution Equation. (5th September 2022)

• Record Type: Journal Article
• Authors: Abuasbeh, Kinda; Shafqat, Ramsha; Niazi, Azmat Ullah Khan; Awadalla, Muath
• Other Names: Morgado Luisa Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2022(2022)
• Publication Date: 2022-09-05
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2022/7512754
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : For fuzzy fractional functional evolution equations, the concept of global and local existence and uniqueness will be presented in this work. We employ the contraction principle and successive approximations for global and local existence and uniqueness, respectively, as given 0 c D q H x I = f I, x I + ∫ 0 I g I, s, x s ds, I ≥ I 0, I ∈ 0, T, x I = ψ I − I 0 = ψ 0 ∈ C σ, I 0 ≥ I ≥ I 0 − σ, x ′ I = ψ ′ I = ψ 1, where C σ denotes the set of fuzzy continuous mapping defined on I 0 − σ, T and σ > 1 . We also use this method to solve fuzzy fractional functional evolution equations with fuzzy population models and distributed delays using fuzzy fractional functional evolution equations. To explain these results, some theorems are given. Finally, certain fuzzy fractional functional evolution equations are illustrated.