The extension of Buckley-Feuring solutions for non-polynomial fuzzy partial differential equations

TL;DR

This paper extends the Buckley-Feuring method to solve fuzzy partial differential equations involving non-polynomial operators, broadening its applicability to more complex fuzzy PDEs.

Contribution

It introduces a natural extension of the Buckley-Feuring approach for non-polynomial fuzzy PDEs, including new assumptions and conditions.

Findings

Extended Buckley-Feuring method for non-polynomial FPDEs

Provides new assumptions and conditions for the extended method

Broadens the scope of fuzzy PDE solutions

Abstract

This paper presents the natural extension of Buckley-Feuring method proposed in \cite{BuckleyFeuring99} for solving fuzzy partial differential equations (FPDE) in a non-polynomial relation, such as the operator $\varphi(D_{x_1}, D_{x_2})$, which maps to the quotient between both partials. The new assumptions and conditions proceedings from this consideration are given in this document.