Journal ArticleDOI
A boundary value problem for second order fuzzy differential equations
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TLDR
A two-point boundary value problem for a second order fuzzy differential equation is interpreted by using a generalized differentiability concept and the problem of finding new solutions is investigated.Abstract:
In this paper, we interpret a two-point boundary value problem for a second order fuzzy differential equation by using a generalized differentiability concept. We present a new concept of solutions and, utilizing the generalized differentiability, we investigate the problem of finding new solutions. Some examples are provided for which the new solutions are found.read more
Citations
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Journal ArticleDOI
Numerical solution of systems of second-order boundary value problems using continuous genetic algorithm
TL;DR: The numerical results show that the proposed continuous genetic algorithm is a robust and accurate procedure for solving systems of second-order boundary value problems and the obtained accuracy for the solutions using CGA is much better than the results obtained using some modern methods.
Journal ArticleDOI
Application of reproducing kernel algorithm for solving second-order, two-point fuzzy boundary value problems
TL;DR: This paper investigates the analytic and approximate solutions of second-order, two-point fuzzy boundary value problems based on the reproducing kernel theory under the assumption of strongly generalized differentiability.
Journal ArticleDOI
On the fractional differential equations with uncertainty
Sadia Arshad,Vasile Lupulescu +1 more
TL;DR: Agarwal et al. as discussed by the authors introduced the concept of fuzzy differential equations of fractional order and proved the existence and uniqueness of solutions of fuzzy fractional differential equations using this concept.
Journal ArticleDOI
Fuzzy fractional differential equations under generalized fuzzy Caputo derivative
TL;DR: The related theorems and properties of fuzzy Caputo fractional differential equation FCFDE under the Generalized Hukuhara differentiability are proved in detail and the method is illustrated by solving some examples.
Journal ArticleDOI
Hukuhara differentiability of interval-valued functions and interval differential equations on time scales
TL;DR: Using the concept of the generalized Hukuhara difference, the differentiability and the integrability for the interval-valued functions on time scales are introduced and studied.
References
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Journal ArticleDOI
Fuzzy differential equations
TL;DR: F fuzzy-set-valued mappings of a real variable whose values are normal, convex, upper semicontinuous and compactly supported fuzzy sets in Rn are studied and the existence and uniqueness theorem for a solution to a fuzzy differential equation is given.
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Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations
Barnabás Bede,Sorin G. Gal +1 more
TL;DR: generalized concepts of differentiability (of any order n@?N), which solves this shortcoming of fuzzy number differentiability, are introduced and some concrete applications to partial and ordinary fuzzy differential equations with fuzzy input data of the form c@?g(x).
Journal ArticleDOI
Metric spaces of fuzzy sets
Phil Diamond,Peter E. Kloeden +1 more
TL;DR: In this article, two classes of metrics for spaces of fuzzy sets are introduced and their equivalence and basic properties established, and a characterisation of compact and locally compact subsets is given in terms of boundedness and p-mean equileft-continuity.
Book
Applications of Fuzzy Sets to Systems Analysis
TL;DR: One of the objects of this book was to facilitate communication by bringing toge- ther different viewpoints and coloring them from a common viewpoint.
Journal ArticleDOI
On the concept of solution for fractional differential equations with uncertainty
TL;DR: In this article, the authors consider a differential equation of fractional order with uncertainty and present the concept of solution, which extends, for example, the cases of first order ordinary differential equations and of differential equations with uncertainty.