آخرین مطالب
امکانات وب
Abstract
In this paper, we further develop Podlubny’s matrix approach to discretization of integrals and derivatives of noninteger order. Numerical integration and differentiation on nonequidistant grids is introduced and illustrated by several examples of numerical solution of differential equations with fractional derivatives of constant orders and with distributedorder derivatives. In this paper, for the first time, we present a variablesteplength approach that we call ‘the method of large steps’, because it is applied in combination with the matrix approach for each ‘large step’. This new method is also illustrated by an easytofollow example. The presented approach allows fractionalorder and distributedorder differentiation and integration of nonuniformly sampled signals, and opens the way to development of variableand adaptivesteplength techniques for fractionaland distributedorder
differential equations.
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