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Zbl 1216.34003
Existence of solutions for fractional differential equations of order $q \in (2,3]$ with anti-periodic boundary conditions.
(English)
[J] J. Appl. Math. Comput. 34, No. 1-2, 385-391 (2010). ISSN 1598-5865; ISSN 1865-2085/e

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 2000:
*34A08
34B15 Nonlinear boundary value problems of ODE
34B18 Positive solutions of nonlinear boundary value problems
47N20 Appl. of operator theory to differential and integral equations

Keywords: fractional differential equations; anti-periodic boundary condition; existence of solution; contraction principle; Krasnoselskii's theorem; positive solution

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