Existence and Uniqueness of Mild Solution for Fractional-Order Controlled Fuzzy Evolution Equation

Author:

Iqbal Naveed1ORCID,Niazi Azmat Ullah Khan23,Shafqat Ramsha3ORCID,Zaland Shamsullah4ORCID

Affiliation:

1. Department of Mathematics, College of Science, University of Ha’il, 81481 Ha’il, Saudi Arabia

2. Faculty of Mathematics and Computational Science, Xiangtan University, Hunan 411105, China

3. Department of Mathematics and Statistics, University of Lahore, Sargodha, Pakistan

4. Faculty of Mathematics, Kabul Polytechnic University, Afghanistan

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.

Publisher

Hindawi Limited

Subject

Analysis

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