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Zbl 1208.34009
McRae, F.A.
Monotone method for periodic boundary value problems of Caputo fractional differential equations. (English)
[J] Commun. Appl. Anal. 14, No. 1, 73-79 (2010). ISSN 1083-2564

Using the Lyapunov Schmidt method, the author develops a monotone iterative technique for the periodic boundary value problems of Caputo fractional differential equations $$^cD^qx=f(t,x),\quad x(0)=x(2 \pi),$$ where $f \in C([0,2 \pi] \times \mathbb{R}, \mathbb{R}),$ $^cD^qx$ is the Caputo derivative of $x$ of order $q$, $0<q<1$. The existence of extremal solutions for the problem is proved by using this monotone iterative technique.
[J. Vasundhara Devi (Visakhapatnam)]

MSC 2000:: *34A45 Theoretical approximation of solutions of ODE
34B15 Nonlinear boundary value problems of ODE
34A08

Keywords: fractional differential equation; existence; extremal solutions; monotone iterative technique

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