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

Authors:
Juan J. Nieto;Rosana Rodríguez-López;Manuel Villanueva-Pesqueira
Affiliations:
Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela, Santiago de Compostela, Spain 15782;Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela, Santiago de Compostela, Spain 15782;Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela, Santiago de Compostela, Spain 15782
Venue:
Fuzzy Optimization and Decision Making
Year:
2011

Citing 20
Cited 1

Fuzzy differential equations

Fuzzy Sets and Systems - Fuzzy Numbers
The Cauchy problem for fuzzy differential equations

Fuzzy Sets and Systems
Differential Inclusions: Set-Valued Maps and Viability Theory

Differential Inclusions: Set-Valued Maps and Viability Theory
Brief note on the variation of constants formula for fuzzy differential equations

Fuzzy Sets and Systems
Optimal impulsive harvesting policy for single population

Nonlinear Analysis: Real World Applications
Global attractivity of positive periodic solutions for an impulsive delay periodic model of respiratory dynamics

Journal of Computational and Applied Mathematics
First order linear fuzzy differential equations under generalized differentiability

Information Sciences: an International Journal
Periodic boundary value problem for first-order impulsive functional differential equations

Computers & Mathematics with Applications
Periodic boundary value problems for impulsive fuzzy differential equations

Fuzzy Sets and Systems
Monotone method for fuzzy differential equations

Fuzzy Sets and Systems
Two-point boundary value problems of undamped uncertain dynamical systems

Fuzzy Sets and Systems
Comparation between some approaches to solve fuzzy differential equations

Fuzzy Sets and Systems
On a class of fuzzy functional differential equations

Fuzzy Sets and Systems
Towards fuzzy differential calculus part 3: Differentiation

Fuzzy Sets and Systems
A note on “two-point boundary value problems associated with non-linear fuzzy differential equations”

Fuzzy Sets and Systems
Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations

Fuzzy Sets and Systems
Variation of constant formula for first order fuzzy differential equations

Fuzzy Sets and Systems
Time-dependent differential inclusions, cocycle attractors and fuzzy differential equations

IEEE Transactions on Fuzzy Systems
Periodicity in a generalized ecological competition system governed by impulsive differential equations with delays

Mathematical and Computer Modelling: An International Journal
Existence and global attractivity of positiveperiodic solution of periodic single-species impulsive Lotka-Volterra systems

Mathematical and Computer Modelling: An International Journal

A new approach for the optimal fuzzy linear time invariant controlled system with fuzzy coefficients

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

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.