Existence of Solutions for the Impulsive Semilinear Fuzzy Intergrodifferential Equations with Nonlocal Conditions and Forcing Term with Memory in n-dimensional Fuzzy Vector Space(ENn, dε)

This article addresses exact controllability for Caputo fuzzy fractional evolution equations in the credibility space from the perspective of the Liu process. The class or problems considered here are Caputo fuzzy differential equations with Caputo derivatives of order β∈(1,2), 0CDtβu(t,ζ)=Au(t,ζ)+f(t,u(t,ζ))dCt+Bx(t)Cx(t)dt with initial conditions u(0)=u0,u′(0)=u1, where u(t,ζ) takes values from U(⊂EN),V(⊂EN) is the other bounded space, and EN represents the set of all upper semi-continuously convex fuzzy numbers on R. In addition, several numerical solutions have been provided to verify the correctness and effectiveness of the main result. Finally, an example is given, which expresses the fuzzy fractional differential equations.

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“…The β-level of u t is then obtained by substituting this expression into (12). After that, all conditions described in Theorem 2 are satisfied.…”

Section: Exact Controllability For Fuzzy Fractional Evolution Equationsmentioning

confidence: 99%

“…These are useful for analyzing phenomena where there is an inherent impression. Solutions of uniqueness and existence for fuzzy equations have been studied by Kwun et al [11,12] and Lee et al [13].…”

Section: Introductionmentioning

confidence: 99%

Controllability for Fuzzy Fractional Evolution Equations in Credibility Space

et al. 2021

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“…They are useful for understanding phenomena that have an underlying effect. Kwun et al [8] and Lee et al [9] investigated the solution of uniqueness-existence for FDEs. Controlled processes have been explored by several researchers.…”

Section: Introductionmentioning

confidence: 99%

Existence Results of Fuzzy Delay Impulsive Fractional Differential Equation by Fixed Point Theory Approach

Khan

Shafqat

Niazi

2022

Journal of Function Spaces

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The main aim of this article is to study controllability and existence of solution of fuzzy delay impulsive fractional nonlocal integro-differential equation in the sense of Caputo operator. The existence and uniqueness of the solution have been carried out with the help of the Banach fixed point theorem. Moreover, for fuzzy fractional differential equations (FFDEs) driven by the Liu process, this present work introduced a concept of stability in credibility space. Finally, efficient examples are presented to demonstrate the main theoretical findings.

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“…Therefore, finding an efficient and accurate algorithm for investigating fuzzy integral equation has recently garnered significant attention among researchers. The existence and uniqueness of the solution of the nonlinear FIDE and impulsive semi-linear FIDEs with nonlocal conditions and forcing the term with memory is well addressed in [12,13]. Recently, Padmapriya et al [14] investigated the numerical solutions of fuzzy fractional delay differential equations using the proposed novel technique.…”

Section: Introductionmentioning

confidence: 99%

Study of Nonlinear Fuzzy Integro-differential Equations Using Mathematical Methods and Applications

Ahmad¹,

Iqbal²,

Hassan³

2021

IJFIS

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In this study, the homotopy perturbation sumudu transform method (HPSTM) is employed to find the analytical fuzzy solution of nonlinear fuzzy integro-differential equations (FIDEs). The solutions of FIDEs are more generalized and have better applications. The fuzzy concept is used to overrule the uncertainty in physical models. Based on the parametric form of the fuzzy number, the nonlinear integro-differential equation (IDE) is converted into two systems of nonlinear IDEs of the second kind. Some numerical examples were solved to demonstrate the efficiency and capability of the method. Graphical representations reveal the symmetry between lower and upper cut representations of fuzzy solutions and may be helpful for a better understanding of fuzzy control models, artificial intelligence, medical science, quantum optics, measure theory, and so on.

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Existence of Solutions for the Impulsive Semilinear Fuzzy Intergrodifferential Equations with Nonlocal Conditions and Forcing Term with Memory in n-dimensional Fuzzy Vector Space(E_Nⁿ, d_ε)

Cited by 4 publications

References 12 publications

Controllability for Fuzzy Fractional Evolution Equations in Credibility Space

Controllability for Fuzzy Fractional Evolution Equations in Credibility Space

Existence Results of Fuzzy Delay Impulsive Fractional Differential Equation by Fixed Point Theory Approach

Study of Nonlinear Fuzzy Integro-differential Equations Using Mathematical Methods and Applications

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