Hybrid fractional-order optimal control problem for immuno-chemotherapy with gene therapy and time-delay: numerical treatments

M. M.Abou Hasan, S. M. AL-Mekhlafi, K. Udhayakumar, F. A. Rihan

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

This paper investigates the optimal control problem for the tumor-immune system with time-delay in the presence of gene therapy and immuno chemotherapy. Riemann-Liouville fractional order integrals and Caputo fractional order derivatives are combined to form a hybrid fractional order operator. For consistency with the physical model problem, a new parameter (Formula presented.) is presented. A stability and bifurcation analysis of the proposed model is performed. The positivity, boundedness, and existence of optimal control for the proposed model are discussed. Grünwald-Letnikov nonstandard finite difference method with the discretization of the hybrid fractional order operator is constructed to solve the proposed model. Examples and comparative studies are presented to demonstrate the simplicity of the approximation approaches and the applicability of the utilized methods.

Original languageEnglish
JournalInternational Journal of Modelling and Simulation
DOIs
Publication statusAccepted/In press - 2023

Keywords

  • Bifurcation analysis
  • Caputo proportional constant fractional derivative
  • Gene and chemotherapy
  • Immunotherapy
  • Nonstandard finite difference method
  • Optimal control problem
  • Stability

ASJC Scopus subject areas

  • Modelling and Simulation
  • General Mathematics
  • Mechanics of Materials
  • General Engineering
  • Hardware and Architecture
  • Industrial and Manufacturing Engineering
  • Electrical and Electronic Engineering

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