Numerical Solution of Linear Multi-Term Initial Value Problems of Fractional Order

In this paper, a new algorithm for the numerical solution of the initial value problems for general linear multi-term dierential equations of frac-tional order with constant coecients and fractional derivatives dened in the Caputo sense is presented. The algorithm essentially uses some ideas from the convolution quadrature and discretized operational calculus. An-other basic element of the method is the formulas for analytical solution of the problem under consideration given in terms of the Mittag-Leer type functions. Error estimates and numerical examples are presented. Special attention is given to the comparison of the numerical results obtained by the new algorithm with those found by other known methods. Mathematics Subject Classication: 26A33, 45J05, 65D20, 65D30 Key Words and Phrases: fractional dierential equations, convolution quadra-ture, Caputo fractional derivative, Mittag-Leer type function