On contraction principle applied to nonlinear fractional differential equations with derivatives of order $\alpha \in (0,1)$
Volume 95 / 2011
Banach Center Publications 95 (2011), 325-338
MSC: Primary 34A08; Secondary 26A33.
DOI: 10.4064/bc95-0-19
Abstract
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.
