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In this paper, we investigate the existence and multiplicity of positive solutions for nonlinear fractional differential equation boundary value problem:
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Numerical Solution of the Bagley-Torvik Equation   总被引：3，自引：0，他引：3
We consider the numerical solution of the Bagley-Torvik equation Ay(t) + BD * 3/2 y(t) + Cy(t) = f(t), as a prototype fractional differential equation with two derivatives. Approximate solutions have recently been proposed in the book and papers of Podlubny in which the solution obtained with approximate methods is compared to the exact solution. In this paper we consider the reformulation of the Bagley-Torvik equation as a system of fractional differential equations of order 1/2. This allows us to propose numerical methods for its solution which are consistent and stable and have arbitrarily high order. In this context we specifically look at fractional linear multistep methods and a predictor-corrector method of Adams type.  相似文献
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We consider a differential equation of fractional order with uncertainty and present the concept of solution. It extends, for example, the cases of first order ordinary differential equations and of differential equations with uncertainty. Some examples are presented.  相似文献
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This paper is concerned with the boundary value problem of a nonlinear fractional differential equation.By means of Schauder fixed-point theorem,an existence result of solution is obtained.  相似文献
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Our main concern here is to give a numerical scheme to solve a nonlinear multi-term fractional (arbitrary) orders differential equation.  相似文献
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Analysis of a system of fractional differential equations   总被引：2，自引：0，他引：2
We prove existence and uniqueness theorems for the initial value problem for the system of fractional differential equations , where Dα denotes standard Riemann-Liouville fractional derivative, 0<α<1, and A is a square matrix. The unique solution to this initial value problem turns out to be , where Eα denotes the Mittag-Leffler function generalized for matrix arguments. Further we analyze the system , , 0<α<1, and investigate dependence of the solutions on the initial conditions.  相似文献
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In this paper we study the asymptotic properties of d-dimensional linear fractional differential equations with time delay. We present necessary and sufficient conditions for asymptotic stability of equations of this type using the inverse Laplace transform method and prove polynomial decay of stable solutions. Two examples illustrate the obtained analytical results.  相似文献