## Existence of solutions for fractional differential equations of order $$q \in (2,3]$$ with anti-periodic boundary conditions.(English)Zbl 1216.34003

The authors consider a fractional order differential equation of order $$q$$, which lies between 2 and 3, with anti-periodic boundary conditions. They establish existence and uniqueness of solutions to fractional order differential equations with anti-periodic boundary conditions and for the two-point boundary value problem by using contraction mapping principal. They also prove the existence of at least one positive solution for the two-point fractional boundary value problem by using Krasnosel’skii’s fixed point theorem. Finally, the existence and uniqueness of solutions of the anti periodic boundary value problem is explained by an example.

### MSC:

 34A08 Fractional ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations 47N20 Applications of operator theory to differential and integral equations
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### References:

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