Solving optimal control problems of Fredholm constraint optimality via the reproducing kernel Hilbert space method with error estimates and convergence analysis

Abstract

Modeling of dynamic systems of optimal control problems (OCPs) is very important issue in applied sciences and engineering. In this analysis, by developed the reproducing kernel Hilbert space (RKHS) method within the calculus of variations, the OCP is solved with respect to initial conditions and Fredholm operator optimality. The solution methodology involves the use of two generalized Hilbert spaces (HSs) for both range and domain spaces. Numerical algorithm and procedure of solution are assembled compatibility with the optimal formulation of the problem. The convergence analysis and error rating of the utilized method are considered under some presumptions, which provide the theoretical structure behind the technique. The optimal profiles show the performance of the numerical solutions and the effect of the Fredholm operator in the optimal results. In this approach, computational simulations are introduced to delineate the suitability, straightforwardness, and relevance of the calculations created.

Fractional-Order Modelling and Optimal Control of Cholera Transmission

“…Modelling dynamic control systems optimally is a very important issue in applied sciences and engineering [30]. In this section, our aim is to minimise the number of cholera infected individuals and, simultaneously, to reduce the associated cost.…”

On a Neutral Itô and Arbitrary (Fractional) Orders Stochastic Differential Equation with Nonlocal Condition

“…Consider the stochastic differential equation Easily, the problem (17) with nonlocal integral conditions (18) satisfies all the assumptions (B1)-(B6) of Theorem 1 with b = 1 120 , c = 1 36 , q = 1 30 then there exists at least one solution to the problem (17) on [0, 1 2 ].…”

“…The results are important since they cover nonlocal generalizations of differential SDEs, and more applications are arising in fields such as heat conduction, electromagnetic theory and dynamical systems and in materials with memory (see, e.g., [9][10][11][12][13][14][15][16][17]), optimal fractional problems and numerical models (see, e.g., [18][19][20][21]).…”

Mathematical modeling of COVID-19 pandemic in India using Caputo-Fabrizio fractional derivative

“…Due to the important property of memory impact of fractional differential operators, the fractional calculus is an effective tool to provide the mathematical demonstration of nature-related truths, natural processes, and processes involving non-local dynamics behaviors. Researchers have developed new efficient models via fractional calculus [ 3 , 6 , 7 , 12 , 26 , 27 ].…”