A Fuzzy Transform Method for Numerical Solution of Fractional Volterra Integral Equations

Agheli, Bahram; Firozja, M. Adabitabar

doi:10.1007/s40819-019-0758-0

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2021

2022

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Cited by 4 publications

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“…The existence and uniqueness of the solutions in the case of fractional integral equations is usually studied by using fixed point theorems (see [1], [8], [11] and [28]). The properties of the solutions were obtained in [25] and [42] and some numerical methods using quadrature schemes, product integration, variational iteration, and fuzzy transforms can be found in [11], [13], [34], [40] and [4], respectively. When such models involves uncertainty, the use of fuzzy sets is suitable, motivating the attention for fuzzy fractional differential and integral equations.…”

Section: Introductionmentioning

confidence: 99%

Numerical Method for Fractional Fuzzy Integral Equations

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Satmari

2021

Preprint

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In the present work we construct an iterative method for the numerical solution of fuzzy fractional Volterra integral equations, by using the technique of fuzzy product integration. The existence and uniqueness of the solution and the uniform boundedness of the terms of the Picard iterations are proved. The convergence of the iterative algorithm is obtained and the apriori error estimate is given in terms of the Lipschitz constants. A numerical example illustrates the accuracy of the method.

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