Local and Global Existence and Uniqueness of Solution for Class of Fuzzy Fractional Functional Evolution Equation

Author:

Abuasbeh Kinda1ORCID,Shafqat Ramsha2ORCID,Niazi Azmat Ullah Khan2ORCID,Awadalla Muath1ORCID

Affiliation:

1. Department of Mathematics and Statistics, College of Science, King Faisal University, Hafuf, Al Ahsa 31982, Saudi Arabia

2. Department of Mathematics and Statistics, The University of Lahore, Sargodha 40100, Pakistan

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.

Funder

Deanship of Scientific Research, Vice Presidency for Graduate Studies and Scientific Research, King Faisal University

Publisher

Hindawi Limited

Subject

Analysis

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