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

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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.

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Authors and Affiliations

  1. Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela, 15782, Santiago de Compostela, Spain

    Juan J. Nieto, Rosana Rodríguez-López & Manuel Villanueva-Pesqueira

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  1. Juan J. Nieto
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  2. Rosana Rodríguez-López
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  3. Manuel Villanueva-Pesqueira
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Correspondence to Rosana Rodríguez-López.

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Nieto, J.J., Rodríguez-López, R. & Villanueva-Pesqueira, M. Exact solution to the periodic boundary value problem for a first-order linear fuzzy differential equation with impulses. Fuzzy Optim Decis Making 10, 323–339 (2011). https://doi.org/10.1007/s10700-011-9108-3

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