Generalized Moore‐Gibson‐Thompson thermoelastic fractional derivative model without singular kernels for an infinite orthotropic thermoelastic body with temperature‐dependent properties

Source abstract

Abstract Many challenges in different applied fields of research, such as materials science, viscoelasticity, biological sciences, physics, and mechanical engineering, require the study of derivative operators using single singular or nonsingular kernels. Atangana and Baleanu (AB) constructed a novel fractional derivative without a singular kernel based on the extended Mittag–Leffler function to overcome the singular kernel problem seen in previous definitions of fractional‐order derivatives. In this article, we provide a novel mathematical thermoelastic heat conduction model that includes the fractional AB derivative operators. In addition, the Moore–Gibson–Thompson (MGT) equation has been incorporated into the proposed heat transport model. The proposed model has been applied to study an infinite orthotropic material with a cylindrical aperture, and the thermal conductivity coefficient of the body depends on the temperature change. The Laplace transform approach has been used to solve the system of governing partial differential equations (PDEs). To assess the validity of the proposed model and for the purposes of comparison, the numerical results have been depicted in figures as well as in tables.