A novel existence and uniqueness theorem for solutions to FDEs driven by Lius process with weak Lipschitz coefficients

Subject Areas : Applied Mathematics

S. Siah-Mansouri ¹ , O. Solaymani Fard ² , M. M. Gachpazan ³

1 - Department of Applied Mathematics, Faculty of Mathematics Sciences, Ferdowsi University of Mashhad, Mashhad, Iran.
2 - Department of Applied Mathematics, School of Mathematics and Computer Science, Damghan University, Damghan.
3 - Department of Applied Mathematics, Faculty of Mathematics Sciences, Ferdowsi University of Mashhad, Mashhad, Iran.

Received: 2016-11-06 Accepted : 2017-01-12 Published : 2017-12-01

Keywords: fuzzy numbers, fuzzy differential equation, Liu's process, Credibility space condition,

Abstract :

This paper we investigate the existence and uniqueness of solutions to fuzzydierential equations driven by Liu's process. For this, it is necessary to provideand prove a new existence and uniqueness theorem for fuzzy dierential equationsunder weak Lipschitz condition. Then the results allows us to considerand analyze solutions to a wide range of nonlinear fuzzy dierential equationsdriven by Liu's process.