Analyticity and uniqueness of the fractional electromagnetic boundary value problem

Abstract

This paper introduces a new study that examines the unique and analytical nature of the fractional solution to a fractional electromagnetic boundary value problem (BVP). This specific BVP is characterized by defining the tangential electromagnetic components. It has been proven that the analytical expressions for the fractional electromagnetic fields $ E^{\alpha} $, $ E^{*\alpha} $, $ H^{\alpha} $, and $ H^{*\alpha} $ do not vanish in any subregions $ \Omega_o^\alpha $ or $ \Omega^\alpha-\Omega_o^\alpha $. Furthermore, the unique solution makes $ E^{\alpha} = E^{*\alpha} $ and $ H^{\alpha} = H^{*\alpha} $ without singular fields at same region of the space. Analyticity of the fractional time-harmonic electromagnetic field within lossy or lossless dielectric regions is proven.

Keywords

• electromagnetic
• analyticity
• uniqueness
• fractional
• bvp