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Using the Euler's method to solve ordinary differential equations of higher order with a mixture of integer and Caputo derivatives

Błaszczyk T., Leszczyński J. S.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2007

Vol. 6, nr 1

31-40

In this paper we present an application of the Euler's method to the numerical solution of fractional ordinary differential equations. These equations include both a classical differential operator of integer order and the fractional one defined in the Caputo sense. Our previous work was limited to the order of fractional derivative α ∈ (0,1) . This study considers numerical schemes for higher orders of a fractional derivative. We then compare our schemes with analytical solutions in order to show their good numerical precision.