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<p>For the purpose of solving fractional differential equations (FDEs), the Formable Integral Transform is a mathematical tool that provides an effective substitute for traditional transforms like the Laplace and Sumudu transforms. In this work, we examine a number of fractional-order mathematical models, such as Newton’s law of cooling, the logistic equation, and the blood alcohol content model, using the Formable integral transform. The Caputo, Caputo-Fabrizio (CF), Atangana-Baleanu-Caputo (ABC), and constant proportional Caputo CPC derivatives are examples of fractional derivatives that are included in these models. Using the Formable transform, we derive analytical solutions and provide graphical representations to investigate how different fractional orders affect the dynamics of the system. Our results demonstrate the Formable integral transform’s efficiency and adaptability in resolving challenging fractional differential equations and improving our comprehension of how systems modelled with various fractional operators behave.</p>

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On Formable integral transform with applications to fractional order mathematical models

  • 期刊论文

  • 发表日期：

    2026年1月3日

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  • Ali Akgül,
  • Mohd Khalid,
  • Nourhane Attia

摘要

For the purpose of solving fractional differential equations (FDEs), the Formable Integral Transform is a mathematical tool that provides an effective substitute for traditional transforms like the Laplace and Sumudu transforms. In this work, we examine a number of fractional-order mathematical models, such as Newton’s law of cooling, the logistic equation, and the blood alcohol content model, using the Formable integral transform. The Caputo, Caputo-Fabrizio (CF), Atangana-Baleanu-Caputo (ABC), and constant proportional Caputo CPC derivatives are examples of fractional derivatives that are included in these models. Using the Formable transform, we derive analytical solutions and provide graphical representations to investigate how different fractional orders affect the dynamics of the system. Our results demonstrate the Formable integral transform’s efficiency and adaptability in resolving challenging fractional differential equations and improving our comprehension of how systems modelled with various fractional operators behave.