Space-time non-local analysis of a porous thermoelastic hollow cylinder using a heat conduction model featuring a Goufo-Caputo two-parameter fractional derivative with phase lags
Ahmed E. Abouelregal, Marín Marín, Abdelaziz Foul, Sameh Askar
Abstract
Fractional derivatives have received considerable attention in modeling thermoelastic behavior due to their ability to reflect memory effects and non-local interactions. In this paper, we introduce a novel thermoelastic model designed to explore the behavior of porous materials featuring voids. This advanced framework builds upon the fractional phase lag thermoelastic model by integrating a two-parameter Mittag-Leffler kernel. An important enhancement over conventional elastic models is the inclusion of both spatial and temporal non-local effects, which are essential for accurately capturing the intricate microscopic interactions characteristic of porous structures. Furthermore, the addition of the Goufo-Caputo two-parameter fractional derivative into the heat conduction equation has improved the representation of memory effects, providing a more comprehensive understanding of how historical deformations and thermal conditions impact material behavior. By evaluating temperature, displacement, stress, and volume fraction fields, this study highlights the strengths and weaknesses of these fractional operators, shedding light on their significance in advancing thermoelastic modeling.