A hybrid of the fractional Vieta–Lucas functions and its application in constrained fractional optimal control systems containing delay

Abstract

In this investigation, a novel framework is devised to study an important category of fractional-order systems. The fractional Vieta–Lucas functions (FVLFs) and a hybrid of the block-pulse functions (BPFs) with the mentioned functions are introduced. The advantages of the proposed basis are clarified and a novel integral operator is further constructed based on the Riemann–Liouville integral operator. An innovative spectral collocation methodology is introduced. By utilizing the new fractional basis, the principal problem is changed into a simple optimization one containing unspecified parameters. The developed discretization scheme is robust and produces very satisfactory results for constrained complex physical systems containing delays. Four benchmark problems are examined to verify the capability of the method. The experimental outputs certify the exactness and usefulness of the new methodology.