A THEORETICAL ANALYSIS ON THE FRACTIONAL FUZZY CONTROLLED EVOLUTION EQUATION

Naeem Saleem; Ramsha Shafqat; Reny George; Azhar Hussain; Muhammad Yaseen

doi:10.1142/S0218348X2340090X

A THEORETICAL ANALYSIS ON THE FRACTIONAL FUZZY CONTROLLED EVOLUTION EQUATION

Naeem Saleem, Ramsha Shafqat, Reny George, Azhar Hussain, Muhammad Yaseen

Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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.

Original language	English
Article number	2340090
Journal	Fractals
Volume	31
Issue number	10
DOIs	https://doi.org/10.1142/S0218348X2340090X
State	Published - 2023

Keywords

Existence
Fractional Evolution Equations
Fuzzy Neutral Differential Equation
Fuzzy Semigroup
Generator of a Fuzzy Semigroup
Mild Solution

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title = "A THEORETICAL ANALYSIS ON THE FRACTIONAL FUZZY CONTROLLED EVOLUTION EQUATION",

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{\textquoteright}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.",

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AU - George, Reny

AU - Hussain, Azhar

AU - Yaseen, Muhammad

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N2 - 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.

AB - 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.

KW - Existence

KW - Fractional Evolution Equations

KW - Fuzzy Neutral Differential Equation

KW - Fuzzy Semigroup

KW - Generator of a Fuzzy Semigroup

KW - Mild Solution

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JO - Fractals

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A THEORETICAL ANALYSIS ON THE FRACTIONAL FUZZY CONTROLLED EVOLUTION EQUATION

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Keywords

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