Modeling and Advance Analysis on the Network of Militants with Mittag-Leffler kernel

Abstract

Many real-world problems are analyzed by using this generalized kind of fractional derivative such as fractal-fractional derivative. In this essay, the detrimental effects on human life and economic considerations are illustrated through an analysis of the militant network’s mathematical model. In order to investigate the effects of militants on society, an epidemic model with a time-fractional order was used to characterise a militant network. The suggested model’s existence and uniqueness are demonstrated using equilibrium analysis. A qualitative study as well as a sensitivity analysis of the fractional order system are conducted. Another method for assessing the local and global impacts of militancy on society is the Ulam-Hyres stability. Additionally, the Lipschitz condition and linear growth model are employed to satisfy the uniqueness of the exact solution criterion. Two-step Lagrange polynomials with Mittag-Leffler kernels are used to find solutions, which show how the illness affects plants by examining the effects of fractional operators. To comprehend how the militant network model behaves, simulations have been created. In order to reduce the number of militants and the danger of terrorism, decision-makers will be able to create circumstances based on the parameters of the model with the aid of this analysis. This research supports the United Nation SDG 16 (Peace, Justice and Strong Institutions) by developing militant’s network model with appropriate level of policing measures. © 2025 NSP Natural Sciences Publishing Cor.