Fractional Taylor Series for Caputo Fractional Derivatives. Construction of Numerical Schemes

@inproceedings{Usero2008FractionalTS,
  title={Fractional Taylor Series for Caputo Fractional Derivatives. Construction of Numerical Schemes},
  author={David Dom{\'i}nguez Usero},
  year={2008}
}
A fractional power series expansion is obtained for Caputo fractional derivative as a generalization of Taylor power series. The series obtained are independent from the point in which fractional derivative is defined. This is used to obtain Euler and Taylor numerical schemes to solve ordinary fractional differential equations. Finally the methods derived are applied to integrate numerically a first and a second order ordinary fractional differential equation using schemes of order α, 2α and 4… CONTINUE READING

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