A Mathematical Modeling of Time-Fractional Maxwell’s Equations Under the Caputo Definition of a Magnetothermoelastic Half-Space Based on the Green–Lindsy Thermoelastic Theorem
This study has established and resolved a new mathematical model of a homogeneous, generalized, magnetothermoelastic half-space with a thermally loaded bounding surface, subjected to ramp-type heating and supported by a solid foundation where these types of mathematical models have been widely used...
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MDPI AG
2025-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/13/9/1468 |
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| author | Eman A. N. Al-Lehaibi |
| author_facet | Eman A. N. Al-Lehaibi |
| author_sort | Eman A. N. Al-Lehaibi |
| collection | DOAJ |
| description | This study has established and resolved a new mathematical model of a homogeneous, generalized, magnetothermoelastic half-space with a thermally loaded bounding surface, subjected to ramp-type heating and supported by a solid foundation where these types of mathematical models have been widely used in many sciences, such as geophysics and aerospace. The governing equations are formulated according to the Green–Lindsay theory of generalized thermoelasticity. This work’s uniqueness lies in the examination of Maxwell’s time-fractional equations via the definition of Caputo’s fractional derivative. The Laplace transform method has been used to obtain the solutions promptly. Inversions of the Laplace transform have been computed via Tzou’s iterative approach. The numerical findings are shown in graphs representing the distributions of the temperature increment, stress, strain, displacement, induced electric field, and induced magnetic field. The time-fractional parameter derived from Maxwell’s equations significantly influences all examined functions; however, it does not impact the temperature increase. The time-fractional parameter of Maxwell’s equations functions as a resistor to material deformation, particle motion, and the resulting magnetic field strength. Conversely, it acts as a catalyst for the stress and electric field intensity inside the material. The strength of the main magnetic field considerably influences the mechanical and electromagnetic functions; however, it has a lesser effect on the thermal function. |
| format | Article |
| id | doaj-art-d05c3e8969eb4639a98f829a4b5292fc |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-d05c3e8969eb4639a98f829a4b5292fc2025-08-20T01:49:11ZengMDPI AGMathematics2227-73902025-04-01139146810.3390/math13091468A Mathematical Modeling of Time-Fractional Maxwell’s Equations Under the Caputo Definition of a Magnetothermoelastic Half-Space Based on the Green–Lindsy Thermoelastic TheoremEman A. N. Al-Lehaibi0Mathematics Department, Jamoum University College, Umm Al-Qura University, Jamoum 25375, Saudi ArabiaThis study has established and resolved a new mathematical model of a homogeneous, generalized, magnetothermoelastic half-space with a thermally loaded bounding surface, subjected to ramp-type heating and supported by a solid foundation where these types of mathematical models have been widely used in many sciences, such as geophysics and aerospace. The governing equations are formulated according to the Green–Lindsay theory of generalized thermoelasticity. This work’s uniqueness lies in the examination of Maxwell’s time-fractional equations via the definition of Caputo’s fractional derivative. The Laplace transform method has been used to obtain the solutions promptly. Inversions of the Laplace transform have been computed via Tzou’s iterative approach. The numerical findings are shown in graphs representing the distributions of the temperature increment, stress, strain, displacement, induced electric field, and induced magnetic field. The time-fractional parameter derived from Maxwell’s equations significantly influences all examined functions; however, it does not impact the temperature increase. The time-fractional parameter of Maxwell’s equations functions as a resistor to material deformation, particle motion, and the resulting magnetic field strength. Conversely, it acts as a catalyst for the stress and electric field intensity inside the material. The strength of the main magnetic field considerably influences the mechanical and electromagnetic functions; however, it has a lesser effect on the thermal function.https://www.mdpi.com/2227-7390/13/9/1468electromagnetismMaxwell’s equationsfractional derivativesCaputo definitionramp-type heatmagnetothermoelasticity |
| spellingShingle | Eman A. N. Al-Lehaibi A Mathematical Modeling of Time-Fractional Maxwell’s Equations Under the Caputo Definition of a Magnetothermoelastic Half-Space Based on the Green–Lindsy Thermoelastic Theorem Mathematics electromagnetism Maxwell’s equations fractional derivatives Caputo definition ramp-type heat magnetothermoelasticity |
| title | A Mathematical Modeling of Time-Fractional Maxwell’s Equations Under the Caputo Definition of a Magnetothermoelastic Half-Space Based on the Green–Lindsy Thermoelastic Theorem |
| title_full | A Mathematical Modeling of Time-Fractional Maxwell’s Equations Under the Caputo Definition of a Magnetothermoelastic Half-Space Based on the Green–Lindsy Thermoelastic Theorem |
| title_fullStr | A Mathematical Modeling of Time-Fractional Maxwell’s Equations Under the Caputo Definition of a Magnetothermoelastic Half-Space Based on the Green–Lindsy Thermoelastic Theorem |
| title_full_unstemmed | A Mathematical Modeling of Time-Fractional Maxwell’s Equations Under the Caputo Definition of a Magnetothermoelastic Half-Space Based on the Green–Lindsy Thermoelastic Theorem |
| title_short | A Mathematical Modeling of Time-Fractional Maxwell’s Equations Under the Caputo Definition of a Magnetothermoelastic Half-Space Based on the Green–Lindsy Thermoelastic Theorem |
| title_sort | mathematical modeling of time fractional maxwell s equations under the caputo definition of a magnetothermoelastic half space based on the green lindsy thermoelastic theorem |
| topic | electromagnetism Maxwell’s equations fractional derivatives Caputo definition ramp-type heat magnetothermoelasticity |
| url | https://www.mdpi.com/2227-7390/13/9/1468 |
| work_keys_str_mv | AT emananallehaibi amathematicalmodelingoftimefractionalmaxwellsequationsunderthecaputodefinitionofamagnetothermoelastichalfspacebasedonthegreenlindsythermoelastictheorem AT emananallehaibi mathematicalmodelingoftimefractionalmaxwellsequationsunderthecaputodefinitionofamagnetothermoelastichalfspacebasedonthegreenlindsythermoelastictheorem |