Аннотация:Part1: Solvability and optimal control problem for impulsive nonlinear fractional dynamic systems.
We study the solvability and optimal controls of an impulsive nonlinear Hilfer fractional delay evolution inclusion in Banach spaces. For the main results, we use fractional calculus, fixed point technique, semigroup theory and multivalued analysis. We introduce the notion of Clarke delay subdifferential. To continue and extend previous works in the field, we prove an existence result of optimal control pair for Lagrange problem LP under appropriate set of sufficient conditions. Finally, as application, we give an impulsive control partial differential inclusion with Hilfer fractional derivative.
Keywords: Optimal control; Hilfer fractional derivative; Delay evolution inclusion; Clarke subdifferential; Impulsive condition.
Part 2: Analysis and approximate controllability for fractional stochastic system of Sobolev type with nonlocal condition We have study the existence and approximate controllability for a class of fractional stochastic dynamic systems of Sobolev type in Hilbert spaces. Fixed point technique, fractional calculus, stochastic analysis and methods adopted directly from deterministic control problems are used for the main results. A suitable set of sufficient conditions for approximate controllability is formulated for the desired results.
Keywords: Fractional calculus; stochastic analysis; approximate controllability; Sobolev type; nonlocal condition.
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