Fractional dynamics of a charged particle in an electromagnetic field

Abstract

In this work, we analyze the modeling of physical phenomena using fractional-order differential equations, specifically focusing on the force exerted on a charged particle in an electromagnetic field. The methodological approach involves replacing integer-order derivatives with fractional-order derivatives, in the Caputo sense, in the differential equations that describe the movement of a charged particle in an electromagnetic field. This allows for a more detailed and efficient description. The results demonstrate that modeling with the Caputo fractional derivative provides a more refined solution, including the presence of damping. It is concluded that the use of fractional calculus offers significant advantages over traditional calculus, particularly in its ability to more accurately capture the system's memory and incorporate factors initially neglected in classical modeling.