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Zbl 1180.34003
Ahmad, Bashir; Sivasundaram, S.
Existence and uniqueness results for nonlinear boundary value problems of fractional differential equations with separated boundary conditions. (English)
[J] Commun. Appl. Anal. 13, No. 1, 121-127 (2009). ISSN 1083-2564

Summary: This paper studies existence and uniqueness results in a Banach space for a two-point boundary value problem involving a nonlinear fractional differential equation given by $${}^cD^qx(t)= f(t,x(t)), \quad 0<t<1,\ 1<q\le 2,$$ $$\alpha x(0)+\beta x'(0)=\gamma_1, \quad \alpha x(1)+\beta x'(1)=\gamma_2.$$ Our results are based on contraction mapping principle and Krasnoselskii's fixed point theorem.

MSC 2000:: *34A08
34B15 Nonlinear boundary value problems of ODE
26A33 Fractional derivatives and integrals (real functions)

Keywords: nonlinear fractional differential equations; separated boundary conditions; existence; fixed point theorem

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