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Relative controllability analysis of fractional order differential equations with multiple time delays. (English) Zbl 1510.93052

Summary: This paper is concerned with the relative controllability for a class of fractional differential equations with multiple time delays. The solution representation is introduced for this system via multiple delayed perturbations of Mittag-Leffler function. Necessary and sufficient conditions for the indicated problem to be relatively controllable are established for linear and non-linear systems. For non-linear case, the existence result is proved by using Krasnoselskii’s fixed point theorem. Numerical examples are given to illustrate the theoretical results, and its diagrammatic formulations are done by MATLAB.

MSC:

93B05 Controllability
34K37 Functional-differential equations with fractional derivatives
93C23 Control/observation systems governed by functional-differential equations

Software:

Matlab
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Full Text: DOI

References:

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