半线性时滞模糊微分方程解的存在性
|
摘要
模糊微分方程常用来模拟不确定条件下的变化过程.其理论被广泛的应用在很多不同的实际问题上.本文主要研究半线性时滞模糊微分方程解的存在性.在广义Hukuhara导数的框架下,运用了一个弱压缩映射的不动点定理,将半线性时滞模糊微分方程解的存在性问题转化为算子不动点的存在性问题,从而建立了方程解的存在性定理.文中例子说明了该理论结果的实用性.
Fuzzy differential equations are commonly used to describe the changing process with uncertain conditions. And its theory is widely applied to many different practical problems. The aim of this paper is to study the existence of solutions for semilinear delay fuzzy differential equations. We use a fixed point theorem of weakly contractive mappings to transform the existence of solutions into the existence of fixed points of an operator, and establish the theorem of existence of solutions for the equations. In addition, an example is given to illustrate the applicability of the theoretical results.
Fuzzy differential equations are commonly used to describe the changing process with uncertain conditions. And its theory is widely applied to many different practical problems. The aim of this paper is to study the existence of solutions for semilinear delay fuzzy differential equations. We use a fixed point theorem of weakly contractive mappings to transform the existence of solutions into the existence of fixed points of an operator, and establish the theorem of existence of solutions for the equations. In addition, an example is given to illustrate the applicability of the theoretical results.
引文
[1]Azbelev N V,Maksimov V P,Rakhmatullina L F.Introduction to the Theory of Functional Differential Equations and Applications[M].Cairo:Hindawi Publishing Corporation,2007
[2]Hale J K.Theory of Functional Differential Equations[M].New York:Springer,1997
[3]Kolmanovskii V,Myshkis A.Introduction to the Theory and Applications of Functional Differential Equations[M].Dordrecht:Kluwer Academic Publisher,1999
[4]Kaleva O.A note on fuzzy differential equations[J].Nonlinear Analysis,2006,64(5):895-900
[5]Bede B,Gal S G.Solutions of fuzzy differential equations based on generalized differentiability[J].Communications in Mathematical and Analysis,2010,9(2):22-41
[6]Puri M L,Ralescu D A.Differential of fuzzy functions[J].Journal of Mathematical Analysis and Applications,1983,91(2):552-558
[7]Kaleva O.Fuzzy differential equations[J].Fuzzy Sets and Systems,1987,24(3):301-317
[8]Nieto J J,Rodr′?guez-L′opez R.Applications of contractive-like mapping principles to fuzzy equations[J].Revista Matem′atica Complutense,2006,19(2):361-383
[9]Chalco-Cano Y,Rom′an-Flores H.On new solutions of fuzzy differential equations[J].Chaos,Solitons and Fractals,2008,38(1):112-119
[10]Bede B,Gal S G.Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations[J].Fuzzy Sets and Systems,2005,151(3):581-599
[11]Diamond P,Kloeden P E.Metric Spaces of Fuzzy Sets:Theory and Applications[M].Singapore:World Scientific,1994
[12]Zadeh L A.Fuzzy sets[J].Information and Control,1965,8(3):338-353
[13]Khastan A,Nieto J J,Rodr′?guez-L′opez R.Fuzzy delay differential equations under generalized differentiability[J].Information Sciences,2014,275:145-167
[14]Stefanini L.A generalization of Hukuhara difference and division for interval and fuzzy arithmetic[J].Fuzzy Sets and Systems,2010,161(11):1564-1584
[15]Goetschel R,Voxman W.Elementary fuzzy calculus[J].Fuzzy Sets and Systems,1986,18(1):31-43
[16]Bede B,Stefanini L.Generalized differentiability of fuzzy-valued functions[J].Fuzzy Sets and Systems,2013,230:119-141
[17]Villamizar-Roa E J,Angula-Castillo V,Chalco-Cano Y.Existence of solutions to fuzzy differential equations with generalized Hukuhara derivative via contractive-like mapping principles[J].Fuzzy Sets and Systems,2015,265:24-38
[18]Khastan A,Nieto J J,Rodr′?guez-L′opez R.Variation of constant formula for first order fuzzy differential equations[J].Fuzzy Sets and Systems,2011,177(1):20-33
[19]Harjani J,Sadarangani K.Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations[J].Nonlinear Analysis:Theory,Methods&Applications,2010,72(3-4):1188-1197
[20]Chalco-Cano Y,Rojas-Medary M A,Rom′an-Flores H.Sobre ecuaciones diferenciales difusas[J].SeMAJournal Boletin de la Sociedad Espa?nola de Matem′atica Aplicada,2007,41:91-100
[2]Hale J K.Theory of Functional Differential Equations[M].New York:Springer,1997
[3]Kolmanovskii V,Myshkis A.Introduction to the Theory and Applications of Functional Differential Equations[M].Dordrecht:Kluwer Academic Publisher,1999
[4]Kaleva O.A note on fuzzy differential equations[J].Nonlinear Analysis,2006,64(5):895-900
[5]Bede B,Gal S G.Solutions of fuzzy differential equations based on generalized differentiability[J].Communications in Mathematical and Analysis,2010,9(2):22-41
[6]Puri M L,Ralescu D A.Differential of fuzzy functions[J].Journal of Mathematical Analysis and Applications,1983,91(2):552-558
[7]Kaleva O.Fuzzy differential equations[J].Fuzzy Sets and Systems,1987,24(3):301-317
[8]Nieto J J,Rodr′?guez-L′opez R.Applications of contractive-like mapping principles to fuzzy equations[J].Revista Matem′atica Complutense,2006,19(2):361-383
[9]Chalco-Cano Y,Rom′an-Flores H.On new solutions of fuzzy differential equations[J].Chaos,Solitons and Fractals,2008,38(1):112-119
[10]Bede B,Gal S G.Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations[J].Fuzzy Sets and Systems,2005,151(3):581-599
[11]Diamond P,Kloeden P E.Metric Spaces of Fuzzy Sets:Theory and Applications[M].Singapore:World Scientific,1994
[12]Zadeh L A.Fuzzy sets[J].Information and Control,1965,8(3):338-353
[13]Khastan A,Nieto J J,Rodr′?guez-L′opez R.Fuzzy delay differential equations under generalized differentiability[J].Information Sciences,2014,275:145-167
[14]Stefanini L.A generalization of Hukuhara difference and division for interval and fuzzy arithmetic[J].Fuzzy Sets and Systems,2010,161(11):1564-1584
[15]Goetschel R,Voxman W.Elementary fuzzy calculus[J].Fuzzy Sets and Systems,1986,18(1):31-43
[16]Bede B,Stefanini L.Generalized differentiability of fuzzy-valued functions[J].Fuzzy Sets and Systems,2013,230:119-141
[17]Villamizar-Roa E J,Angula-Castillo V,Chalco-Cano Y.Existence of solutions to fuzzy differential equations with generalized Hukuhara derivative via contractive-like mapping principles[J].Fuzzy Sets and Systems,2015,265:24-38
[18]Khastan A,Nieto J J,Rodr′?guez-L′opez R.Variation of constant formula for first order fuzzy differential equations[J].Fuzzy Sets and Systems,2011,177(1):20-33
[19]Harjani J,Sadarangani K.Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations[J].Nonlinear Analysis:Theory,Methods&Applications,2010,72(3-4):1188-1197
[20]Chalco-Cano Y,Rojas-Medary M A,Rom′an-Flores H.Sobre ecuaciones diferenciales difusas[J].SeMAJournal Boletin de la Sociedad Espa?nola de Matem′atica Aplicada,2007,41:91-100