Generalized distributed-order fractional optimal control problem using Laguerre wavelet method

Document Type : Research Article

Authors

Department of Mathematics, National Institute of Technology Rourkela, Rourkela-769008, Odisha, India

Abstract

This research presents a novel numerical method for solving a class of complex optimal control problems characterized by distributed-order derivatives. By effectively employing fractional-order Laguerre wavelets, the study transforms the original continuous-time problem into a discrete set of algebraic equations. This transformation is facilitated by the use of Reimann-Liouville distributed-order operational matrices and a carefully chosen set of Newton-Cotes collocation points. The optimized solution is then determined by applying the Lagrange multiplier method to solve the resulting system of equations. The paper rigorously investigates the convergence properties of this approach, establishing error bounds that provide a measure of its accuracy. Finally, the effectiveness of this method is demonstrated through a series of illustrative examples, showcasing its high precision and applicability to a wide range of generalized distributed-order optimal control problems.

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Journal of Mathematical Modeling
Volume 13, Issue 4
December 2025
Pages 747-765

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