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<p>This study investigates conformable electromagnetic field theory by incorporating the principles of conformable calculus. A novel concept, the conformable delta function, is introduced to extend the classical delta function within this framework. This function plays a crucial role in computing Poisson brackets. Building upon this foundation, the conformable Maxwell’s equations are derived, offering a more generalized approach to modeling electromagnetic phenomena, particularly in systems exhibiting non-integer order behavior. The results highlight the potential applications of conformable calculus in electrodynamics, providing new insights for both theoretical and applied research in physics and engineering. Moreover, the traditional Maxwell’s equations are recovered when <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\( \alpha =1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>α</mi> <mo>=</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>.</p>

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The Treatment of Conformable Electromagnetic Theory of Maxwell as a Singular System

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月13日

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  • Eqab M. Rabei,
  • Mohamed Ghaleb Al-Masaeed,
  • Dumitru Baleanu,
  • Sami Muslih

摘要

This study investigates conformable electromagnetic field theory by incorporating the principles of conformable calculus. A novel concept, the conformable delta function, is introduced to extend the classical delta function within this framework. This function plays a crucial role in computing Poisson brackets. Building upon this foundation, the conformable Maxwell’s equations are derived, offering a more generalized approach to modeling electromagnetic phenomena, particularly in systems exhibiting non-integer order behavior. The results highlight the potential applications of conformable calculus in electrodynamics, providing new insights for both theoretical and applied research in physics and engineering. Moreover, the traditional Maxwell’s equations are recovered when \( \alpha =1\) α = 1 .