Existence and uniqueness of solutions for fuzzy fractional Volterra-Fredholm integro-differential equations

Allahviranloo, Tofigh; Armand, A.; Gouyandeh, Z.; Ghadiri, Hassan

doi:10.5899/2013/jfsva-00163

Cited by 25 publications

(7 citation statements)

References 17 publications

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“…A fuzzy fractional integral equation has been investigated in [38]. Fuzzy fractional Volterra-Fredholm integro-differential equations has been introduced in [39]. The exact and approximate solutions have been constructed for fuzzy fractional differential equations in [40].…”

Section: Introductionmentioning

confidence: 99%

Theoretical and practical applications of fuzzy fractional integral sliding mode control for fractional-order dynamical system

2014

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This paper proposes a fuzzy fractional integral sliding mode control for synchronizing fractionalorder dynamical systems with mismatched fractional orders. It is applied to synchronize the fractional-order modified coupled dynamos chaotic systems. Synchronization between two identical fractional order, different fractional orders, integer order and fractional-order modified coupled dynamos chaotic systems have been demonstrated. For practical applications, these derived synchronized fractional-order chaotic systems are utilized to develop a novel cryptosystem for an image encryption and decryption. Numerical simulations are provided to verify the significance of theoretical analysis.

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Section: Introductionmentioning

confidence: 99%

Theoretical and practical applications of fuzzy fractional integral sliding mode control for fractional-order dynamical system

2014

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“…In 2012, Allahviranloo et al [5] studied the analytical solution to the initial value problem for a class of Riemann-Liouville-type fractional differential equations under the strong generalized Hukuhara differentiability introduced in [8]. Then Allahviranloo et al studied the initial value problem of the Volterra-Fredholm-type fuzzy integro-differential equation, and established the existence and uniqueness of the solution by using a compact mapping theorem and an iterative method [3]. Recently, Ngo presented results on the existence and uniqueness of solutions for two kinds of fractional fuzzy functional integral equations and fuzzy functional differential equations using the contraction mapping principle and the successive approximation method [11,12].…”

Section: Introductionmentioning

confidence: 99%

Well-posedness and stability for fuzzy fractional differential equations

Zhang

Xi²,

O’Regan³

2022

NAMC

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In this article, we consider the existence and uniqueness of solutions for a class of initial value problems of fuzzy Caputo–Katugampola fractional differential equations and the stability of the corresponding fuzzy fractional differential equations. The discussions are based on the hyperbolic function, the Banach fixed point theorem and an inequality property. Two examples are given to illustrate the feasibility of our theoretical results.

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“…In 2020, using the concept of kernal ψ-functions, Vu and Hoa [7] investigated the applications of contractive-like mapping principal to fuzzy fractional integral equations. A variety of fuzzy fractional differential and integral equation applications, in different fields of the sciences, such as electrochemistry, physics, economy, chemistry, electromagnetic, viscoelasticity and control theory, are present in the literature-for example, [8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Fixed Point Results via Least Upper Bound Property and Its Applications to Fuzzy Caputo Fractional Volterra–Fredholm Integro-Differential Equations

et al. 2021

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In recent years, complex-valued fuzzy metric spaces (in short CVFMS) were introduced by Shukla et al. (Fixed Point Theory 32 (2018)). This setting is a valuable extension of fuzzy metric spaces with the complex grade of membership function. They also established fixed-point results under contractive condition in the aforementioned spaces and generalized some essential existence results in fixed-point theory. The purpose of this manuscript is to derive some fixed-point results for multivalued mappings enjoying the least upper bound property in CVFMS. Furthermore, we studied the existence theorem for a unique solution to the Fuzzy fractional Volterra–Fredholm integro-differential equations (FCFVFIDEs) as an application to our derived result involving the Caputo derivative.

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Existence and uniqueness of solutions for fuzzy fractional Volterra-Fredholm integro-differential equations

Abstract: In this paper we use the fuzzy Caputo derivatives under generalized Hukuhara difference to introduce fuzzy fractional Volterra-Fredholm integro-differential equations and prove the existence and uniqueness of the solutions for this class of fractional equations.

Cited by 25 publications

References 17 publications

Theoretical and practical applications of fuzzy fractional integral sliding mode control for fractional-order dynamical system

Theoretical and practical applications of fuzzy fractional integral sliding mode control for fractional-order dynamical system

Well-posedness and stability for fuzzy fractional differential equations

Fixed Point Results via Least Upper Bound Property and Its Applications to Fuzzy Caputo Fractional Volterra–Fredholm Integro-Differential Equations

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