Application of generalized Lucas wavelet method for solving nonlinear fractal-fractional optimal control problems

Sedigheh Sabermahani, Yadollah Ordokhani and Parisa Rahimkhani

Chaos, Solitons & Fractals, 2023, vol. 170, issue C

Abstract: Different types of fractional derivatives have recently been noticed by researchers and used in modeling phenomena due to their characteristics. Furthermore, fractional optimal control problems have been the focus of many researchers because they reflect the real nature of different models. Hence, this article considers a class of nonlinear fractal-fractional optimal control problems in the Atangana–Riemann–Liouville sense with the Mittag-Leffler non-singular kernel. In this study, a numerical method based on the generalized Lucas wavelets and the Ritz method is presented to obtain approximate solutions. Then, the generalized Lucas wavelets and an extra pseudo-operational matrix of the Atangana–Riemann–Liouville derivative are introduced. We demonstrate the advantage of the proposed method through three numerical examples.

Keywords: Generalized Lucas wavelets; Fractal-fractional optimal control problems; Ritz method; Atangana–Riemann–Liouville derivative; Pseudo-operational matrix (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:170:y:2023:i:c:s0960077923002497

DOI: 10.1016/j.chaos.2023.113348

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