Investigating fractional derivative coefficients in optimal control problems using Bell's polynomials to solve them numerically

Articles in Press

Document Type : Research Paper

Authors
Ayatollah Yari 1
Ahmad Reza Haghighi 2
1 Department of Mathematics, Faculty of Basic Sciences, Payame Noor University, Tehran, Iran
2 Department of Applied Mathematics, Faculty of Mathematical Sciences, Allameh Tabatabai University, Tehran, Iran
10.22075/ijnaa.2025.37264.5448
Abstract
In this research‎, ‎we present a numerical method for solving fractional optimal control problems(FOCPs)‎, ‎and the working method is based on Bell’s polynomial‎. ‎Derivatives and fractional integrals of Caputo and Riemann type have been used‎. ‎To obtain approximate solutions‎, ‎we consider the fractional derivative of the state function and self-control as functions of Bell polynomials with unknown coefficients‎, ‎and in the process of this work‎, ‎we see the emergence of the derivative and integral operator matrices in terms of the fractional parameter‎. Finally‎, ‎using a numerical method such as Lagrangian coefficients‎, ‎the optimal control problem leads to a system of equations‎, ‎from the solution of which all the unknowns will be found‎. ‎All solutions are compared with each other on the basis of ordinary and fractional derivatives, and the results are interesting‎.
Keywords
FOCPs
fractional integration and derivative
Bell Polynomials
Operational matrices
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International Journal of Nonlinear Analysis and Applications

Articles in Press, Corrected Proof
Available Online from 29 September 2026

  • Receive Date 19 April 2025
  • Revise Date 30 July 2025
  • Accept Date 30 July 2025