Mathematics and Computational Sciences

An innovative Bernoulli operational matrix framework for regularized Prabhakar fractional optimal control problems

Document Type : Original Article

Authors

Chaima Boutiba 1, 2
Ahmed Bokhari 2, 1
Rachid Belgacem 1, 3
Dumitru Baleanu 3, 4

1 Faculty of Exact Sciences and Computer Science, Hassiba Benbouali University of Chlef, Algeria.

2 Laboratory of Mathematics and its Applications LMA, Hassiba Benbouali University of Chlef, Algeria.

3 Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon.

4 Institute of Space Sciences, Magurele-Bucharest, Romania.

https://doi.org/10.30511/mcs.2026.2067782.1426
Abstract
This paper introduces a novel operational matrix approach for addressing a class of fractional-order optimal control problems, where the derivative is taken in the regularized Prabhakar sense. The method employs Bernoulli polynomials and utilizes their operational matrix of regularized Prabhakar derivative and inherent properties to convert the original problem into a finite-dimensional optimization problem. Using the Lagrange multiplier approach, the required optimality conditions are derived, yielding an algebraic system from the original problem. Solving this system yields an approximate fractional optimal solution. The practicality and efficiency of the proposed approach are confirmed via a series of numerical examples.

Keywords

Fractional optimal control problems
Regularized Prabhakar derivative
Operational matrix
Lagrange multipliers

Subjects

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Mathematics and Computational Sciences
Volume 7, Issue 1
Winter 2026
Pages 118-137

  • Receive Date 03 August 2025
  • Revise Date 14 December 2025
  • Accept Date 02 January 2026

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