Abstract
In this paper we study the fractional boundary value problem
where \({1 < q < 2, \alpha , \beta \in IR}\) and \({^{c}D_{0^{+}}^{q}}\) denotes the Caputo’s fractional derivative. Using Banach contraction principle and Leray–Schauder nonlinear alternative we prove the existence and uniqueness of solutions. Some examples are given to illustrate our results.
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Guezane-Lakoud, A., Khaldi, R. Solvability of a Three-Point Fractional Nonlinear Boundary Value Problem. Differ Equ Dyn Syst 20, 395–403 (2012). https://doi.org/10.1007/s12591-012-0125-7
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DOI: https://doi.org/10.1007/s12591-012-0125-7
Keywords
- Nonlocal condition
- Fractional Caputo derivative
- Banach contraction principle
- Leray–Schauder nonlinear alternative
- Nontrivial solution