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<p>The main aim of the study is a mathematical model of COVID-19 using the variable Atangana-Baleanu (AB) fractional derivatives with the Mittag-Leffler kernel in the Caputo sense. Only the AB kernel is a crossover for the waiting time distribution from stretched exponential to a power law. The Caputo-Fabrizio (CF) derivative is less noisy. In contrast, the fractional AB derivative provides an excellent description due to its Mittag-Leffler memory, distinguishing between dynamical systems at different scales without a steady state. With the help of the fixed point theory and Picard-Lindelöf method, we explore the existence and uniqueness of the solution for the proposed COVID-19 model. Moreover, we discuss the generalized Ulam-Hyers stability and the generalized Ulam-Hyers-Rassias stability.</p>

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Analysis of COVID-19 Model Using Atangana-Baleanu Variable Order Operator

  • 期刊论文

  • 发表日期：

    2025年10月27日

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  • Pratibha Verma,
  • Surabhi Tiwari

摘要

The main aim of the study is a mathematical model of COVID-19 using the variable Atangana-Baleanu (AB) fractional derivatives with the Mittag-Leffler kernel in the Caputo sense. Only the AB kernel is a crossover for the waiting time distribution from stretched exponential to a power law. The Caputo-Fabrizio (CF) derivative is less noisy. In contrast, the fractional AB derivative provides an excellent description due to its Mittag-Leffler memory, distinguishing between dynamical systems at different scales without a steady state. With the help of the fixed point theory and Picard-Lindelöf method, we explore the existence and uniqueness of the solution for the proposed COVID-19 model. Moreover, we discuss the generalized Ulam-Hyers stability and the generalized Ulam-Hyers-Rassias stability.