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Zbl 1181.34006
Belmekki, Mohammed; Nieto, Juan J.; Rodr{\'\i}guez-López, Rosana
Existence of periodic solution for a nonlinear fractional differential equation. (English)
[J] Bound. Value Probl. 2009, Article ID 324561, 18 p. (2009). ISSN 1687-2770/e

Summary: We consider the following nonlinear fractional differential equation of the form $$D^\delta u(t)-\lambda u(t)=f(t,u(t)),\quad t\in J:=(0,1], \ 0<\delta<1,\tag{1.1}$$ where $D^\delta$ is the standard Riemann-Liouville fractional derivative, $f$ is continuous, and $\lambda\in\Bbb R$. Due to the singularity of the possible solutions, we introduce a new and proper concept of periodic boundary value conditions. We present Green's function and give some existence results for the linear case and then we study the nonlinear problem.

MSC 2000:: *34A08
34C25 Periodic solutions of ODE
34B15 Nonlinear boundary value problems of ODE

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Zentralblatt MATH Berlin [Germany]