The existence of mild solutions and approximate controllability for nonlinear fractional neutral evolution systems. (English) Zbl 07875986
Summary: The existence of mild solutions and approximate controllability for Riemann-Liouville fractional neutral evolution systems with nonlocal conditions of a fractional order is investigated. The Laplace transform and semigroup theory are the tools used to prove the existence. In turn, approximate controllability is proved on the basis of a Nemytskii operator, a Mittag-Leffler function and certain hypotheses using fixed point theorems, as well as the construction of a Cauchy sequence. An example is provided to highlight the main results.
MSC:
| 93B05 | Controllability |
| 93C10 | Nonlinear systems in control theory |
| 93C15 | Control/observation systems governed by ordinary differential equations |
| 26A33 | Fractional derivatives and integrals |
Keywords:
fractional neutral evolution system; approximate controllablity; mild solution; Riemann-Liouville derivativesReferences:
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