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EXISTENCE AND UNIQUENESS OF SOLUTIONS TO A CLASS OF NONLINEAR FRACTIONAL ORDER DIFFERENTIAL EQUATIONS WITH DELAY
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作者 Xiaogang Liu 《Annals of Differential Equations》 2014年第2期157-165,共9页
A class of nonlinear fractional order differential equations with delay is investigated in this paper. Using Leray-Schauder fixed point theorem and the contraction mapping theorem, we obtain some sufficient conditions... A class of nonlinear fractional order differential equations with delay is investigated in this paper. Using Leray-Schauder fixed point theorem and the contraction mapping theorem, we obtain some sufficient conditions for the existence and uniqueness of solutions to the fractional order differential equations. 展开更多
关键词 fractional order differential equations SOLUTION EXISTENCE UNIQUENESS DELAY
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A New Technique for Solving Fractional Order Systems: Hermite Collocation Method 被引量:2
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作者 Nilay Akgonullu Pirim Fatma Ayaz 《Applied Mathematics》 2016年第18期2307-2323,共17页
In this study, we establish an approximate method which produces an approximate Hermite polynomial solution to a system of fractional order differential equations with variable coefficients. At collocation points, thi... In this study, we establish an approximate method which produces an approximate Hermite polynomial solution to a system of fractional order differential equations with variable coefficients. At collocation points, this method converts the mentioned system into a matrix equation which corresponds to a system of linear equations with unknown Hermite polynomial coefficients. Construction of the method on the aforementioned type of equations has been presented and tested on some numerical examples. Results related to the effectiveness and reliability of the method have been illustrated. 展开更多
关键词 fractional order differential equations Hermite Polynomials Hermite Series Collocation Methods
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EXISTENCE OF MILD SOLUTIONS TO SEMILINEAR FRACTIONAL ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS 被引量:4
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作者 Heping Jiang(Dept. of Math.,Huangshan University,Huangshan 245041,Anhui) Wei Jiang(School of Mathematical Science,University of Anhui,Hefei 230039) 《Annals of Differential Equations》 2011年第3期318-322,共5页
In this paper,we use the analytic semigroup theory of linear operators and fixed point method to prove the existence of mild solutions to a semilinear fractional order functional differential equations in a Banach space.
关键词 mild solutions fractional order functional differential equations Banach fixed point theorem analytic semigroup
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EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTIONS TO NONLINEAR DELAY FRACTIONAL DIFFERENTIAL EQUATIONS 被引量:3
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作者 Xiaofei Wu,Xidong Sun(Shandong Institute of Business and Technology,Yantai 264005,Shandong) 《Annals of Differential Equations》 2011年第1期54-61,共8页
Using a fixed point theorem,this paper discusses the existence and uniqueness of positive solutions to a system of nonlinear delay fractional differential equations and obtains some new results.
关键词 differential equation of fractional order positive solution fixed point
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