Positive solutions for boundary value problem of nonlinear fractional differential equation

In this paper, we investigate the existence and multiplicity of positive solutions for nonlinear fractional differential equation boundary value problem:

  

Numerical Solution of the Bagley-Torvik Equation

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.  

On the concept of solution for fractional differential equations with uncertainty

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.  

EXISTENCE OF SOLUTION FOR BOUNDARY VALUE PROBLEM OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION

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.  

Numerical methods for multi-term fractional (arbitrary) orders differential equations

Our main concern here is to give a numerical scheme to solve a nonlinear multi-term fractional (arbitrary) orders differential equation.  

一类次线性分数微分方程的正解存在性

证明了一类非线性项受幂函数控制的次线性分数微分方程的正解存在性.主要方法是锥拉伸与锥压缩型的Krasnosel’skii不动点定理的局部应用.我们的结论表明该方程可以具有一个正解,只要非线性项在某个有界集上的“高度”是适当的.  

Analysis of a system of fractional differential equations

We prove existence and uniqueness theorems for the initial value problem for the system of fractional differential equations , where D^α 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 E_α 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.  

一类分数阶微分方程正解的存在性

研究了非线性项可变号的分数阶微分方程两点边值问题其中f:[0,1]×[0,∞)→（→∞,∞）是连续的,λ>0,q（t）>0₂通过构造适当算子,继而运用锥上的不动点定理,得到了该问题至少一个正解的存在性.  

Asymptotic properties of fractional delay differential equations

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.