Exact solution to the periodic boundary value problem for a first-order linear fuzzy differential equation with impulses

Using the expression of the exact solution to a periodic boundary value problem for an impulsive first-order linear differential equation, we consider an extension to the fuzzy case and prove the existence and uniqueness of solution for a first-order linear fuzzy differential equation with impulses...

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Veröffentlicht in:	Fuzzy optimization and decision making Jg. 10; H. 4; S. 323 - 339
Hauptverfasser:	Nieto, Juan J., Rodríguez-López, Rosana, Villanueva-Pesqueira, Manuel
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Boston Springer US 01.12.2011 Springer Science + Business Media B.V Springer Nature B.V
Schlagworte:	Artificial Intelligence Boundary value problems Calculus of Variations and Optimal Control; Optimization Differential equations Exact solutions Fuzzy Fuzzy logic Fuzzy set theory Fuzzy sets Impulses Impulsivity Mathematical analysis Mathematical Logic and Foundations Mathematics Mathematics and Statistics Operations Research/Decision Theory Optimization Ordinary differential equations Probability Theory and Stochastic Processes Studies Linear fuzzy differential equations Green’s function First-order fuzzy differential equations Periodic boundary value problems
ISSN:	1568-4539, 1573-2908
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Abstract	Using the expression of the exact solution to a periodic boundary value problem for an impulsive first-order linear differential equation, we consider an extension to the fuzzy case and prove the existence and uniqueness of solution for a first-order linear fuzzy differential equation with impulses subject to boundary value conditions. We obtain the explicit solution by calculating the solutions on each level set and justify that the parametric functions obtained define a proper fuzzy function. Our results prove that the solution of the fuzzy differential equation of interest is determined, under the appropriate conditions, by the same Green’s function obtained for the real case. Thus, the results proved extend some theorems given for ordinary differential equations.
AbstractList	Using the expression of the exact solution to a periodic boundary value problem for an impulsive first-order linear differential equation, we consider an extension to the fuzzy case and prove the existence and uniqueness of solution for a first-order linear fuzzy differential equation with impulses subject to boundary value conditions. We obtain the explicit solution by calculating the solutions on each level set and justify that the parametric functions obtained define a proper fuzzy function. Our results prove that the solution of the fuzzy differential equation of interest is determined, under the appropriate conditions, by the same Green's function obtained for the real case. Thus, the results proved extend some theorems given for ordinary differential equations. Using the expression of the exact solution to a periodic boundary value problem for an impulsive first-order linear differential equation, we consider an extension to the fuzzy case and prove the existence and uniqueness of solution for a first-order linear fuzzy differential equation with impulses subject to boundary value conditions. We obtain the explicit solution by calculating the solutions on each level set and justify that the parametric functions obtained define a proper fuzzy function. Our results prove that the solution of the fuzzy differential equation of interest is determined, under the appropriate conditions, by the same Green's function obtained for the real case. Thus, the results proved extend some theorems given for ordinary differential equations.[PUBLICATION ABSTRACT]
Author	Rodríguez-López, Rosana Nieto, Juan J. Villanueva-Pesqueira, Manuel
Author_xml	– sequence: 1 givenname: Juan J. surname: Nieto fullname: Nieto, Juan J. organization: Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela – sequence: 2 givenname: Rosana surname: Rodríguez-López fullname: Rodríguez-López, Rosana email: rosana.rodriguez.lopez@usc.es organization: Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela – sequence: 3 givenname: Manuel surname: Villanueva-Pesqueira fullname: Villanueva-Pesqueira, Manuel organization: Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela
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SubjectTerms	Artificial Intelligence Boundary value problems Calculus of Variations and Optimal Control; Optimization Differential equations Exact solutions Fuzzy Fuzzy logic Fuzzy set theory Fuzzy sets Impulses Impulsivity Mathematical analysis Mathematical Logic and Foundations Mathematics Mathematics and Statistics Operations Research/Decision Theory Optimization Ordinary differential equations Probability Theory and Stochastic Processes Studies
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Title	Exact solution to the periodic boundary value problem for a first-order linear fuzzy differential equation with impulses
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