A THEORETICAL ANALYSIS ON THE FRACTIONAL FUZZY CONTROLLED EVOLUTION EQUATION

Saleem N., Shafqat R., George R., Hussain A., Yaseen M.

Fractals, vol.31, no.10, 2023 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 31 Issue: 10
  • Publication Date: 2023
  • Doi Number: 10.1142/s0218348x2340090x
  • Journal Name: Fractals
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Compendex, INSPEC, zbMATH, DIALNET, Civil Engineering Abstracts
  • Keywords: Existence, Fractional Evolution Equations, Fuzzy Neutral Differential Equation, Fuzzy Semigroup, Generator of a Fuzzy Semigroup, Mild Solution
  • Uşak University Affiliated: No

Abstract

This paper designates two important properties of the existence-uniqueness of the mild solution for a fractional controlled fuzzy evolution equation involving the Caputo-derivative by using nonlocal conditions, where β ∈ (1, 2), and it is formulated as (Formula Presented) where A is a strongly continuous fuzzy semigroup’s generator. Furthermore, many numerical solutions have been presented to ensure that key results are accurate and reliable. Finally, an example about fuzzy fractional evolution equations is presented.