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

Abstract 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 $$ \alpha =1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> .