Toward the existence and uniqueness of solutions of second-order fuzzy volterra integro-differential equations with fuzzy kernel

Allahviranloo, Tofigh; Khezerloo, M.; Sedaghatfar, O.; Salahshour, Soheil

doi:10.1007/s00521-012-0849-x

Cited by 19 publications

(13 citation statements)

References 21 publications

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“…In [13], Allahviranloo et al proposed a new technique to solve the FVIDEs using definition of generalized differentiability. Later, Allahviranloo et al in [14] discussed the existence and uniqueness of second-order FVIDEs using the fuzzy kernel. Then Matinfar et al in [15] solved the FVIDEs using the variational iteration method while Sahu and Saha Ray used Legendre wavelet method in [16].…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Volterra Integro-Differential Equations Using General Linear Method

et al. 2019

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In this paper, a fuzzy general linear method of order three for solving fuzzy Volterra integro-differential equations of second kind is proposed. The general linear method is operated using the both internal stages of Runge-Kutta method and multivalues of a multisteps method. The derivation of general linear method is based on the theory of B-series and rooted trees. Here, the fuzzy general linear method using the approach of generalized Hukuhara differentiability and combination of composite Simpson’s rules together with Lagrange interpolation polynomial is constructed for numerical solution of fuzzy volterra integro-differential equations. To illustrate the performance of the method, the numerical results are compared with some existing numerical methods.

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Section: Introductionmentioning

confidence: 99%

Fuzzy Volterra Integro-Differential Equations Using General Linear Method

et al. 2019

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“…Kaleva [1] studied the Cauchy problem of fuzzy differential equation and characterized those subsets of fuzzy sets in which the Peano theorem is valid. Park et al in [11][12][13][14] have considered the existence of solution of fuzzy integral equation in Banach space. In 2002, Xue and Fu [15] established solutions to fuzzy differential equations with right-hand side functions satisfying Caratheodory conditions on a class of Lipschitz fuzzy sets.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Integral Equations and Strong Fuzzy Henstock Integrals

Shao

Zhang

2014

Abstract and Applied Analysis

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“…However, Goetschel, Jr., and Voxman have proposed the Riemann integral-type approach [6]. Some mathematicians have separately worked on the existence and having a unique solution of fuzzy Volterra integrodifferential equation [7][8][9]. Recently, numerical methods have been applied to solve the linear as well as nonlinear differential equation fuzzy integral equation and fuzzy integrodifferential equation [7,8,[10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%