A THEORETICAL ANALYSIS ON THE FRACTIONAL FUZZY CONTROLLED EVOLUTION EQUATION

Naeem Saleem, Ramsha Shafqat, Reny George, Azhar Hussain and Muhammad Yaseen
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Naeem Saleem: Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan
Ramsha Shafqat: Department of Mathematics and Statistics, University of Lahore, Sargodha 40100, Pakistan
Reny George: Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
Azhar Hussain: Department of Mathematics, University of Chakwal, Chakwal 48800, Pakistan
Muhammad Yaseen: Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan

FRACTALS (fractals), 2023, vol. 31, issue 10, 1-15

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 0cD ωβ𠔲(ω) = 𠒜𠔲(ω) + χ(ω, 𠔲(h(ω))) + 𠒬(ω)ℋ(ω),𠔲(0) = 𠔲0 + (−1)g(𠔲), 𠔲′(0) = 𠔲 1, where 𠒜 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.

Keywords: Mild Solution; Fractional Evolution Equations; Existence; Fuzzy Semigroup; Fuzzy Neutral Differential Equation; Generator of a Fuzzy Semigroup (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X2340090X

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