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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Zusammenfassung: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.
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ISSN:1568-4539
1573-2908
DOI:10.1007/s10700-011-9108-3