Existence, uniqueness, and characterization theorems for nonlinear fuzzy integrodifferential equations of Volterra type
type: Item
instance of: scholarly article
title: Existence, uniqueness, and characterization theorems for nonlinear fuzzy integrodifferential equations of Volterra type
zbMATH Open document ID: 1394.34162
DOI: 10.1155/2015/835891
author: Omar Abu Arqub
author: Shaher Momani
author: Saleh A. Al-Mezel
author: Marwan A. Kutbi
published in: Mathematical Problems in Engineering
publication date: 2018-08-27T00:00:00Z
review text: Summary: Existence and uniqueness theorem are the tool which makes it possible for us to conclude that there exists only one solution to a given problem which satisfies a constraint condition. How does it work? Why is it the case? We believe it, but it would be interesting to see the main ideas behind this. To this end, in this paper, we investigate existence, uniqueness, and other properties of solutions of a certain nonlinear fuzzy Volterra integrodifferential equation under strongly generalized differentiability. The main tools employed in the analysis are based on the applications of the Banach fixed point theorem and a certain integral inequality with explicit estimate. Also, some results for characterizing solution by an equivalent system of crisp Volterra integrodifferential equations are presented. In this way, a new direction for the methods of analytic and approximate solutions is proposed.
Mathematics Subject Classification ID: 34K36
Mathematics Subject Classification ID: 45J05
zbMATH DE Number: 6927350
Wikidata QID: Q59119609
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/835891
OpenAlex ID: W2042459455
cites work: Two-point boundary value problems associated with nonlinear fuzzy differential equations
cites work: Initial and boundary value problems for fuzzy differential equations.
cites work: An Approach to Modelling and Simulation of Uncertain Dynamical Systems
cites work: Two-point boundary value problems of uncertain dynamical systems
cites work: Solution of linear differential equations with fuzzy boundary values
cites work: Fuzzy approximate solutions of second-order fuzzy linear boundary value problems
cites work: Almost periodic fuzzy-number-valued functions
cites work: Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations
cites work: A note on ``Two-point boundary value problems associated with non-linear fuzzy differential equations''
cites work: On new solutions of fuzzy differential equations
cites work: A boundary value problem for second order fuzzy differential equations
cites work: Numerical solution of fuzzy differential equations under generalized differentiability
cites work: Existence and uniqueness of fuzzy solution for the nonlinear fuzzy integrodifferential equations
cites work: On existence and uniqueness of solutions of fuzzy integrodifferential equations
cites work: Q5479519
cites work: Q5190961
cites work: Existence and Uniqueness of Solutions of Fuzzy Volterra Integro-differential Equations
cites work: Existence of global solutions to nonlinear fuzzy Volterra integro-differential equations
cites work: Q5263482
cites work: Numerical algorithm for solving two-point, second-order periodic boundary value problems for mixed integro-differential equations
cites work: Note on ``Numerical solution of fuzzy differential equations by predictor-corrector method''
cites work: Numerical solution of hybrid fuzzy differential equation IVPs by a characterization theorem
cites work: Fuzzy differential equations
cites work: Elementary fuzzy calculus
cites work: Fuzzy random variables
cites work: Differentials of fuzzy functions
cites work: On some fuzzy functional equations
cites work: On Henstock integral of fuzzy-number-valued functions. I
cites work: Integrals of fuzzy-number-valued functions
cites work: On the fuzzy initial value problem
cites work: A note on the extension principle for fuzzy sets
cites work: A note on Zadeh's extensions
cites work: Attractors and asymptotic stability for fuzzy dynamical systems
cites work: Initial value problems for higher-order fuzzy differential equations
cites work: Q5446043
description: scientific article; zbMATH DE number 6927350