Abstract
In this article existence and uniqueness of the solutions of the initial problem for neutral nonlinear differential system with incommensurate order fractional derivatives in Caputo sense and with piecewise continuous initial function is proved. A formula for integral presentation of the general solution of a linear autonomous neutral system with several delays is established and used for the study of the stability properties of a neutral autonomous nonlinear perturbed linear fractional differential system. Natural sufficient conditions are found to ensure that from global asymptotic stability of the zero solution of the linear part of a nonlinearly perturbed system it follows global asymptotic stability of the zero solution of the whole nonlinearly perturbed system.
Highlights
A variety of scientific fields are successfully using the latest advances in fractional calculus and fractional differential equations
We point out that this is due to the fact that, in fractional delay differential equations, the dependence on the past evolution history of the processes described by such equations is inspired by two sources
First of them is the impact conditioned by the delays and the other one the impact conditioned from the availability of Volterra type integral in the definitions of the fractional derivatives, i.e., the memory of the fractional derivative
Summary
A variety of scientific fields are successfully using the latest advances in fractional calculus and fractional differential equations. It must be noted that for the study of the stability properties described above, a formula for integral representation of the general solution of a linear autonomous neutral system with several delays is proved. Using the formula obtained in the previous section, some natural sufficient conditions are found to ensure that from global asymptotic stability of the zero solution of the linear part of a nonlinearly perturbed system it follows global asymptotic stability of the zero solution of the whole nonlinearly perturbed system
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