Existence of solutions for some two-point fractional boundary value problems under barrier strip conditions. (English) Zbl 1524.34021
Summary: In this paper, we are dedicated to researching the boundary value problems (BVPs) for equation \(D^{\alpha}x(t)=f(t,x(t),D^{\alpha -1}x(t))\), with the boundary value conditions to be either: \(x(0)=A, D^{\alpha -1}x(1)=B\) or \(D^{\alpha -1}x(0)=A, x(1)=B\). Let the nonlinear term \(f\) satisfy some sign conditions, then by making use of the Leray-Schauder nonlinear alternative, some existence results are obtained. In the end, an example is given to verify the main results.
MSC:
| 34A08 | Fractional ordinary differential equations |
| 34B15 | Nonlinear boundary value problems for ordinary differential equations |
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