The Influence of the Caputo Fractional Derivative on Time-Fractional Maxwell’s Equations of an Electromagnetic Infinite Body with a Cylindrical Cavity Under Four Different Thermoelastic Theorems

Eman A. N. Al-Lehaibi and Hamdy M. Youssef ()
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Eman A. N. Al-Lehaibi: Mathematics Department, Jamoum University College, Umm Al-Qura University, Jamoum 25375, Saudi Arabia
Hamdy M. Youssef: Mechanical Engineering Department, College of Engineering and Architecture, Umm Al-Qura University, Makkah 21955, Saudi Arabia

Mathematics, 2024, vol. 12, issue 21, 1-22

Abstract: This paper introduces a new mathematical modeling of a thermoelastic and electromagnetic infinite body with a cylindrical cavity in the context of four different thermoelastic theorems; Green–Naghdi type-I, type-III, Lord–Shulman, and Moore–Gibson–Thompson. Due to the convergence of the four theories under study and the simplicity of putting them in a unified equation that includes these theories, the theories were studied together. The bunding plane of the cavity surface is subjected to ramp-type heat and is connected to a rigid foundation to stop the displacement. The novelty of this work is considering Maxwell’s time-fractional equations under the Caputo fractional derivative definition. Laplace transform techniques were utilized to obtain solutions by using a direct approach. The Laplace transform’s inversions were calculated using Tzou’s iteration method. The temperature increment, strain, displacement, stress, induced electric field, and induced magnetic field distributions were obtained numerically and represented in figures. The time-fractional parameter of Maxwell’s equations has a significant impact on all the mechanical studied functions and does not affect the thermal function. The time-fractional parameter of Maxwell’s equations works as a resistance to deformation, displacement, stress, and induced magnetic field distributions, while it acts as a catalyst to the induced electric field through the material.

Keywords: maxwell’s equations; time-fractional; fractional derivatives; thermoelasticity; Caputo definition; electromagnetic; Green–Naghdi; Lord–Shulman; Moore–Gibson–Thompson (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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