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Keywords = generalized fuzzy Euler’s method

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16 pages, 316 KB  
Article
Ulam Stabilities and Instabilities of Euler–Lagrange-Rassias Quadratic Functional Equation in Non-Archimedean IFN Spaces
by Kandhasamy Tamilvanan, Abdulaziz Mohammed Alanazi, John Michael Rassias and Ali H. Alkhaldi
Mathematics 2021, 9(23), 3063; https://doi.org/10.3390/math9233063 - 28 Nov 2021
Cited by 5 | Viewed by 2183
Abstract
In this paper, we use direct and fixed-point techniques to examine the generalised Ulam–Hyers stability results of the general Euler–Lagrange quadratic mapping in non-Archimedean IFN spaces (briefly, non-Archimedean Intuitionistic Fuzzy Normed spaces) over a field. Full article
(This article belongs to the Special Issue Advances in Functional Equations and Convex Analysis)
24 pages, 1504 KB  
Article
A Fuzzy Method for Solving Fuzzy Fractional Differential Equations Based on the Generalized Fuzzy Taylor Expansion
by Tofigh Allahviranloo, Zahra Noeiaghdam, Samad Noeiaghdam and Juan J. Nieto
Mathematics 2020, 8(12), 2166; https://doi.org/10.3390/math8122166 - 4 Dec 2020
Cited by 18 | Viewed by 3910
Abstract
In this field of research, in order to solve fuzzy fractional differential equations, they are normally transformed to their corresponding crisp problems. This transformation is called the embedding method. The aim of this paper is to present a new direct method to solve [...] Read more.
In this field of research, in order to solve fuzzy fractional differential equations, they are normally transformed to their corresponding crisp problems. This transformation is called the embedding method. The aim of this paper is to present a new direct method to solve the fuzzy fractional differential equations using fuzzy calculations and without this transformation. In this work, the fuzzy generalized Taylor expansion by using the sense of fuzzy Caputo fractional derivative for fuzzy-valued functions is presented. For solving fuzzy fractional differential equations, the fuzzy generalized Euler’s method is introduced and applied. In order to show the accuracy and efficiency of the presented method, the local and global truncation errors are determined. Moreover, the consistency, convergence, and stability of the generalized Euler’s method are proved in detail. Eventually, the numerical examples, especially in the switching point case, show the flexibility and the capability of the presented method. Full article
(This article belongs to the Section D2: Operations Research and Fuzzy Decision Making)
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