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Solvability of fractional differential equations with integral boundary conditions at resonance. (English) Zbl 1304.34008

Summary: By using the coincidence degree theory due to Mawhin and constructing suitable operators, some sufficient conditions for the existence of solution for a class of fractional differential equations with integral boundary conditions at resonance are established, which are complement of previously known results. The interesting point is that we shall deal with the case \(\dim\text{Ker\,}L= 2\), which will cause some difficulties in constructing the projector \(Q\). An example is given to illustrate our result.

MSC:

34A08 Fractional ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
47N20 Applications of operator theory to differential and integral equations
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