Fractional calculus is a branch of mathematics that studies the use fractional operators. The evolution computing allowed its application in many areas, including control theory. operators are known to well describe memory phenomena, favorable characteristic for control. Another benefit order these adds more tunable parameters controller, allowing greater flexibility and possibility improving p...

Whooping cough, or pertussis, is an infectious disease that causes serious threats to people of all ages, specifically infant and young children, over the world. Due severe impact on health, it necessary construct a mathematical model can be used predict future dynamics disease, as well suggest strategies eliminate in optimal way. For this, we constructed new Atangana–Baleanu fractional for who...

Abstract This work presents a novel formulation for the numerical solution of optimal control problems related to nonlinear Volterra fractional integral equations systems. A spectral approach is implemented based on new polynomials known as Chelyshkov polynomials. First, properties these are studied solve aforementioned problems. The operational matrices and Galerkin method used discretize cont...

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...

<p style='text-indent:20px;'>We consider optimal control of fractional in time (subdiffusive, i.e., for <inline-formula><tex-math id="M1">\begin{document}$ 0<\gamma <1 $\end{document}</tex-math></inline-formula>) semilinear parabolic PDEs associated with various notions diffusion operators an unifying fashion. Under general assumptions on the nonlinea...

In this work, a fractional-order synthetic drugs transmission model with psychological addicts has been proposed along treatment. The effects of are deadly and sometimes even violent. We have studied the local global stability different criterion. existence uniqueness criterion positivity boundedness solutions also established. stabilities decided by basic reproduction number R0. analyzed sensi...

this paper deals with optimal operation of a three-product dividing-wall column (dwc). the main idea is to design a control structure, through a systematic procedure for plantwide control, with an objective to achieve desired product purities with the minimum use of energy. exact local method is used to find the best controlled variables as single measurement or combination of measurements base...