A New Method for Solving Two-Dimensional Fuzzy Fredholm Integral Equations of The Second Kind

Subject Areas : Applied Mathematics

Mohsen Darabi ¹ , Nouredin Parandin ² , Mahmoud Paripour ³ , Ali Seifi ⁴

1 - Department of Mathematics, Islamic Azad University, Hamedan Branch, Hamedan, Iran
2 - Department of Mathematics, Islamic Azad University, Kermanshah Branch, Kermanshah, Iran.
3 - Department of Mathematics, Hamedan University of Technology, Hamedan, Iran.
4 - Department of Mathematics, Islamic Azad University, Hamedan Branch, Hamedan, Iran.

Received: 2019-12-21 Accepted : 2020-05-05 Published : 2021-12-01

Keywords: Integral Equation, Adomian decomposition, Fuzzy Fredholm, Parametric form,

Abstract :

In this work, we introduce a novel method for solving two-dimensional fuzzy Fredholm integral equationsof the second kind (2D-FFIE-2). We use new representation of parametric form of fuzzy numbers and converta two-dimensional fuzzy Fredholm integral equation to system of two-dimensional Fredholm integral equationsof the second kind in crisp case. We can use Adomian decomposition method for nding the approximationsolution of the each equation, hence obtain an approximation for fuzzy solution of 2D-FFIE-2. We prove theconvergence of the method and nally apply the method to some examples