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Nonlocal Cauchy problems for fractional order nonlinear differential systems

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Wang J., Li X., Zhou Y.

Open Physics

2013

vol. 11

issue 10

1399-1413

In this paper, we discuss nonlocal Cauchy problems for fractional order nonlinear differential systems. Firstly, an important matrix associated with fractional order and two functionals are constructed. Further, some sufficient conditions which guarantee such matrix convergent to zero matrix are presented. Secondly, by using three fixed point theorems via the techniques that use convergent to zero matrix and vector norm, some existence results for the solutions of such fractional order nonlinear differential systems are given under different conditions. Finally, some examples are given to illustrate the results.

Existence of positive solutions for nonlocal boundary value problem of fractional differential equation

100%

Liu X., Lin L., Fang H.

Open Physics

2013

vol. 11

issue 10

1423-1432

In this paper, we study a type of nonlinear fractional differential equations multi-point boundary value problem with fractional derivative in the boundary conditions. By using the upper and lower solutions method and fixed point theorems, some results for the existence of positive solutions for the boundary value problem are established. Some examples are also given to illustrate our results.

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2 Open Physics

2 2013

1 Fang H.

1 Li X.

1 Lin L.

1 Liu X.

1 Wang J.

1 Zhou Y.

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Nonlocal Cauchy problems for fractional order nonlinear differential systems

Existence of positive solutions for nonlocal boundary value problem of fractional differential equation