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

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.

Fractional Temperature-Dependent BEM for Laser Ultrasonic Thermoelastic Propagation Problems of Smart Nanomaterials

“…To demonstrate the numerical computations calculated using the proposed methodology, we consider the temperature-dependent thermoelastic smart nanomaterial properties of pure copper (Cu) nanoparticles [40,41] as shown in Table 1 and using the boundary conditions depicted in Figure 2 to exemplify the numerical computations computed by the suggested methodology. Under thermal and piezoelectric loadings, the considered thermoelastic smart nanomaterial deforms and becomes electrically polarized.…”

Fractional Temperature-Dependent BEM for Laser Ultrasonic Thermoelastic Propagation Problems of Smart Nanomaterials

“…By using Kirchhoff transformation 𝑇= ( ) 𝑑Θ [30], Eq. ( 22) may be written as follows [31] ∇ 𝑇(𝐱, τ) + 1 𝜆 ℎ(𝐱, 𝑇, τ) = 𝜌 𝑐 𝜆 𝜕𝑇(𝐱, τ) 𝜕τ +𝑁𝑙 𝐱,𝑇,𝑇 (41) which can be expressed as [31] ∇ 𝑇(𝐱, τ) + 1 𝜆 ℎ 𝐱, 𝑇, 𝑇 ,τ = 𝜌 𝑐 𝜆 𝜕𝑇(𝐱, τ) 𝜕τ (42) in which…”

On Multiple-Type Wave Solutions for the Nonlinear Coupled Time-Fractional Schrödinger Model

“…Fractional-order derivatives offer advantages over integer derivatives, providing more accurate mathematical and physical models for various technical issues [25][26][27]. Consequently, fractional NLSE models have become essential for understanding soliton dynamics in optical fibers, with various solution schemes developed over the past two decades [28][29][30][31][32][33][34][35][36][37][38][39]. The motivation behind this study stems from the growing need to address complex nonlinear phenomena across diverse scientific disciplines, particularly in optics and applied sciences.…”