MODELING TELECOMMUNICATION SUBSCRIBER FRAUD HEALING DYNAMICS USING FRACTIONAL CALCULUS

Abstract

Telecommunication subscriber fraud significantly threatens the financial health and operational integrity of telecom providers. Common forms—such as subscription fraud, bypass fraud, and identity manipulation—exploit system vulnerabilities for unauthorized gains, leading to substantial financial losses, reduced customer trust, and service disruptions. While fraud detection has been widely studied, limited attention is paid to fraud healing dynamics, the process by which networks recover from such incidents. Classical integer-order differential models fail to capture the non-local, memory-dependent nature of fraud recovery. To address this gap, we propose a modeling framework based on fractional calculus, which extends traditional calculus to non-integer orders and effectively models long-memory and hereditary behaviors. We introduce a fractional differential equation (FDE) model specific to fraud recovery in telecom systems, showing its superiority over classical models. Parametric analysis and simulations highlight how detection delays and recovery efforts influence healing. This model supports intelligent, resilient fraud management strategies