Numerical solution of fractional variational and optimal control problems via fractional-order Chelyshkov functions

Abstract

<abstract><p>In this paper, we present a new numerical method based on the fractional-order Chelyshkov functions (FCHFs) for solving fractional variational problems (FVPs) and fractional optimal control problems (FOCPs). The fractional derivatives are considered in the Caputo sense. The operational matrix of fractional integral for FCHFs, together with the Lagrange multiplier method, are used to reduce the fractional optimization problem into a system of algebraic equations. Some results concerning the approximation errors are discussed and the convergence of the presented method is also demonstrated. The performance of the introduced method is tested through several examples. Some comparisons with recent numerical methods are introduced to show the accuracy and effectiveness of the presented method.</p></abstract>

Generalized model of stochastic common property fishery differential game: Numerical study

“…In this section, inspired by Ahmed, and Al-Ahmary [4] and Ahmed et al [5], we intend to define the FSCPs on the arbitrary interval [a, b]. To do this, we consider the mapping κ α : [a, b] −→ [0, 1] as:…”

“…As mentioned in Section 1, all results for infinite-horizon case with θ = 1 2 are analytical, which can be obtained from (5). The value of performance index in x 0 = 20 is W * = 11.90315098.…”

“…Fractional-order Chelyshkov collocation method (FCCM) was applied for solving systems of fractional differential equations in [4]. This method was also used for finding numerical solution of fractional variational and optimal control problems in [5]. Nikooeinejad and Heydari in [40] employed shifted fractional-order Legendre collocation method to solve HJB PDEs in stochastic optimal control Problems.…”