Analyticity and uniqueness of the fractional electromagnetic boundary value problem

A. Refaie Ali; Rashid Jan; H. Alotaibi; Nesreen A. Yaseen; A. Refaie Ali; Rashid Jan; H. Alotaibi; Nesreen A. Yaseen

doi:10.3934/mmc.2024009

Mathematical Modelling and Control

2024, Volume 4, Issue 1: 101-109. doi: 10.3934/mmc.2024009

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Research article

Analyticity and uniqueness of the fractional electromagnetic boundary value problem

1.
Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Shebin El Kom 32511, Menofia Governorate, Egypt
2.
Institute of Energy Infrastructure, Department of Civil Engineering, College of Engineering, Universiti Tenaga Nasional, Putrajaya Campus, Jalan IKRAM-UNITEN, Kajang 43000, Selangor, Malaysia
3.
Mathematics Research Center, Near East University, Mersin 10, Nicosia 99138, Turkey
4.
Department of Mathematics and Statistics, Faculty of Science, Taif University, P. O. Box 11099, Taif 21944, Saudi Arabia
5.
Higher Instiute for Computers and Information Technology, El Shorouk, Cairo, Egypt

Received: 26 August 2023 Revised: 06 December 2023 Accepted: 25 December 2023 Published: 01 April 2024

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.
- electromagnetic,
- analyticity,
- uniqueness,
- fractional,
- BVP
Citation: A. Refaie Ali, Rashid Jan, H. Alotaibi, Nesreen A. Yaseen. Analyticity and uniqueness of the fractional electromagnetic boundary value problem[J]. Mathematical Modelling and Control, 2024, 4(1): 101-109. doi: 10.3934/mmc.2024009

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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.

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