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Abstract
In this article, we use a fuzzy number in its parametric form to solve a fuzzy nonlinear integral equation of the second kind in the crisp case. The main theme of this article is to find a semi-analytical solution of fuzzy nonlinear integral equations. A hybrid method of Laplace transform coupled with Adomian decomposition method is used to find the solution of the fuzzy nonlinear integral equations including fuzzy nonlinear Fredholm integral equation, fuzzy nonlinear Volterra integral equation, and fuzzy nonlinear singular integral equation of Abel type kernel. We also provide some suitable examples to better understand the proposed method.
Highlights
The notions of fuzzy differential equations (FDEs) and fuzzy integral equations (FIEs) with fuzzy control have attracted the researchers
Zadeh introduced the concept of fuzzy set [1], followed by that of fuzzy number, and implemented it in fuzzy control [2] and approximate reasoning [3, 4]
Motivated by the aforesaid work, in this article, we use a hybrid method of Laplace transform coupled with Adomian decomposition method to solve the fuzzy nonlinear integral equation of the type β1 (h) ω(h, γ ) = f (h, γ ) + μ
Summary
The notions of fuzzy differential equations (FDEs) and fuzzy integral equations (FIEs) with fuzzy control have attracted the researchers. A dire need is to develop a numerical procedure and mathematical models that would deal with the general fuzzy integral equations and solve them appropriately. Various applications and methods for solving linear and nonlinear integral equations are given in [42]. Wu and Ma [19] provided the first application of fuzzy integral and investigated fuzzy Fredholm integral equation of the second kind (FF-2), while Park et al [45] showed the existence of a solution of FIEs. A large amount of research work has been done to investigate FIEs [46,47,48,49,50,51,52,53,54,55,56,57].
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