Journal of Computational Applied Mechanics

Variational approach to optimal control constrained by fractal-fractional differential equations

Document Type : Research Paper

Authors

1 School of Information Engineering, Yango University, Fuzhou 350015, China

2 School of Science, Xi'an University of Architecture and Technology, Xi’an 710055, China

3 School of Jia Yang, Zhejiang Shuren University, Shaoxing 312028, China

4 Department of Mathematical Sciences, Saveetha School of Engineering, SIMATS, Chennai, Tamil Nadu, India

Abstract

The extant corpus of literature pertaining to optimal control problems with partial differential equation (PDE) constraints is extensive. This paper introduces a novel variational approach to optimal control problems constrained by fractal-fractional differential equations. Utilizing the shallow water wave as a case study, the semi-inverse method is employed to establish the variational formulation. This approach not only exemplifies a novel mode of thinking but also has significant ramifications for the field. This novel approach to optimal control paves a promising path for further research and provides researchers and practitioners with a novel perspective and potential avenues for further exploration. By exploring this alternative approach, researchers and practitioners can develop a more profound understanding of the fundamental nature of optimal control problems and identify more effective solutions for a wide range of applications.

Keywords

Main Subjects

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Journal of Computational Applied Mechanics
Volume 56, Issue 3
July 2025
Pages 602-610
  • Receive Date: 06 June 2025
  • Accept Date: 06 June 2025