This paper investigates some duality results of a mixed type for class multiple objective fractional optimal control problems. More precisely, by considering the Wolfe- and Mond–Weir-type dualities, we formulate robust mixed-type dual problem and, under suitable convexity assumptions involved functionals, establish equivalence between solution sets considered models. Essentially, investigate we...

The paper deals with an optimal control problem in a dynamical system described by linear differential equation the Caputo fractional derivative. goal of is to minimize Bolza-type cost functional, which consists two terms: first one evaluates state at fixed terminal time, and second integral evaluation on whole time interval. In order solve this problem, we propose reduce it some auxiliary firs...

In this paper, we examine the unique solvability (in sense of strong solutions) Cauchy problem for a linear inhomogeneous equation in Banach space solved with respect to Caputo fractional derivative. We assume that operator acting on unknown function right-hand side generates an analytic resolving family corresponding homogeneous equation. obtain representation solution and optimal control prob...

The aim of this study is to introduce a novel method solve class two-dimensional fractional optimal control problems. Since there are some difficulties solving these problems using analytical methods, thus finding numerical methods approximate their solution challenging topic. In study, we use transcendental Bernstein series. fact, for the problem, generalize polynomials larger functions which ...