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Zbl 1216.34003
Ahmad, Bashir
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.
[K. Rajendra Prasad (Visakhapatnam)]

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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