Solving fuzzy Volterra integro-differential equation by fuzzy differential transform method

Mikaeilvand, Nasser; Khakrangin, Sakineh; Allahviranloo, Tofigh

doi:10.2991/eusflat.2011.56

Cited by 12 publications

(7 citation statements)

References 5 publications

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“…The existence and uniqueness of solutions of FIDEs were investigated by Park and Jeong in [16], Hajighasemi et al in [7], and Zeinali et al in [17]. Mikaeilvand et al in [15] presented the numerical examples of FIDEs using the differential transform method. In [1,2], Allahviranloo et al proposed a new technique to solve the FIDEs using definition of generalized differentiability.…”

Section: Introductionmentioning

confidence: 99%

Numerical solutions of fuzzy integro-differential equations of the second kind

Issa¹

2020

J. Math. Computer Sci.

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Section: Introductionmentioning

confidence: 99%

Numerical solutions of fuzzy integro-differential equations of the second kind

Issa¹

2020

J. Math. Computer Sci.

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“…Sell and Miller have analyzed the second kind of Volterra integral equations [24]. The fuzzy Volterra integro-differential equations (FVIDEs) have been studied by Mikaeilvand et al [25].…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Fractional Order Volterra-Fredholm Integro-Differential Equations Using MADM

KASIMALA

Chakraverty

2022

Preprint

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This paper investigates solutions to the fractional integro-differential equation (FIDE) of fuzziness. Here we consider, In the Caputo sense, we look at the fuzzy fractional Volterra-Fredholm integro-differential equation (CFFVFIDE) and use fixed point theory to prove its existence and uniqueness. Moreover, we apply the modified Adomian decomposition method (MADM) to find a solution to the presented problem, and to support our approach, we offer a few examples. We also give visual analysis to see how the solutions behave. 2010 MSC: 26A33, 35R09, 34A07, 45J05.

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“…The existence and uniqueness of FIDEs and FVIDEs solutions were investigated by Park and Jeong in [9], Hajighasemi et al in [10], and Zeinali et al in [11]. Mikaeilvand et al in [12] presented the numerical examples of FVIDEs using the differential transform method. In [13], Allahviranloo et al proposed a new technique to solve the FVIDEs using definition of generalized differentiability.…”

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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Solving fuzzy Volterra integro-differential equation by fuzzy differential transform method

Cited by 12 publications

References 5 publications

Numerical solutions of fuzzy integro-differential equations of the second kind

Numerical solutions of fuzzy integro-differential equations of the second kind

Fuzzy Fractional Order Volterra-Fredholm Integro-Differential Equations Using MADM

Fuzzy Volterra Integro-Differential Equations Using General Linear Method

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