On contraction principle applied to nonlinear fractional differential equations with derivatives of order $\alpha \in (0,1)$

Volume 95 / 2011

Małgorzata Klimek Banach Center Publications 95 (2011), 325-338 MSC: Primary 34A08; Secondary 26A33. DOI: 10.4064/bc95-0-19


One-term and multi-term fractional differential equations with a basic derivative of order $\alpha \in (0,1)$ are solved. The existence and uniqueness of the solution is proved by using the fixed point theorem and the equivalent norms designed for a given value of parameters and function space. The explicit form of the solution obeying the set of initial conditions is given.


  • Małgorzata KlimekInstitute of Mathematics
    Częstochowa University of Technology
    Dąbrowskiego 73
    42-200 Częstochowa, Poland

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