The Caputo-, Riemann-Liouville-, and Grünwald-Letnikov-type difference initial value problems for linear fractional-order systems are discussed. We take under our consideration the possible solutions via the classicalZ-transform method. We stress the formula for the image of the discrete Mittag-Leffler matrix function in theZ-transform. We also prove forms of images in theZ-transform of the expressed fractional difference summation and operators. Additionally, the stability problem of the considered systems is studied.
The paper develops further the algebraic formalism for nonlinear control systems defined on homogeneous time scales. The delta derivative operator is extended to differential p-forms and vector fields.
Abstract:In the paper possible approximation of solutions to initial value problems stated for fractional nonlinear equations with sequential derivatives of Caputo type is presented.
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