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Volume 31
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10.3390/mca31030105
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

A Modified Time-Fractional Lord–Shulman Approach to Thermoelasticity in Hollow Spheres with Variable Thermal Conductivity

by
Ashraf M. Zenkour
1,*,
Noha M. Seyam
2 and
Maryam H. Aljadani
3
1
Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2
Department of Mathematics, College of Applied Sciences, Umm Al-Qura University, P.O. Box 21955, Makkah 715, Saudi Arabia
3
Department of Mathematics, Jamoum University College, Umm Al-Qura University, Jamoum 25375, Saudi Arabia
*
Author to whom correspondence should be addressed.
Math. Comput. Appl. 2026, 31(3), 105; https://doi.org/10.3390/mca31030105 (registering DOI)
Submission received: 25 April 2026 / Revised: 29 May 2026 / Accepted: 10 June 2026 / Published: 12 June 2026
Versions Notes

Abstract

This study investigates a 2D fractional order generalized thermoelastic problem in a homogeneous and isotropic thermoelastic hollow sphere. The sphere is exposed to a decaying heat source, and the governing equations are derived using a refined fractional-order Lord–Shulman (LS) model of generalized thermoelasticity. The Laplace transform technique is used to convert time-dependent PDEs into simpler ODEs in the Laplace domain. Its numerical inversion method is used to revert to the time domain. Numerical simulations are carried out to investigate the distributions of temperature, displacement, and stress fields within the hollow sphere. The obtained results reveal that both the fractional-order parameter and the variable thermal conductivity strongly affect the thermoelastic response, particularly the propagation characteristics of thermal waves, stress intensity, and relaxation behavior. In addition, the curvature of the hollow geometry plays an important role in modifying the radial and circumferential stress distributions and their attenuation throughout the medium.
Keywords: hollow sphere; fractional-order; LS theory; decaying heat source; variable thermal conductivity hollow sphere; fractional-order; LS theory; decaying heat source; variable thermal conductivity

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MDPI and ACS Style

Zenkour, A.M.; Seyam, N.M.; Aljadani, M.H. A Modified Time-Fractional Lord–Shulman Approach to Thermoelasticity in Hollow Spheres with Variable Thermal Conductivity. Math. Comput. Appl. 2026, 31, 105. https://doi.org/10.3390/mca31030105

AMA Style

Zenkour AM, Seyam NM, Aljadani MH. A Modified Time-Fractional Lord–Shulman Approach to Thermoelasticity in Hollow Spheres with Variable Thermal Conductivity. Mathematical and Computational Applications. 2026; 31(3):105. https://doi.org/10.3390/mca31030105

Chicago/Turabian Style

Zenkour, Ashraf M., Noha M. Seyam, and Maryam H. Aljadani. 2026. "A Modified Time-Fractional Lord–Shulman Approach to Thermoelasticity in Hollow Spheres with Variable Thermal Conductivity" Mathematical and Computational Applications 31, no. 3: 105. https://doi.org/10.3390/mca31030105

APA Style

Zenkour, A. M., Seyam, N. M., & Aljadani, M. H. (2026). A Modified Time-Fractional Lord–Shulman Approach to Thermoelasticity in Hollow Spheres with Variable Thermal Conductivity. Mathematical and Computational Applications, 31(3), 105. https://doi.org/10.3390/mca31030105

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