Study of Generalized Two-Temperature Magneto Thermoelastic Problem Involving Memory Dependent Derivative under Fuzzy Environment

A generalized two-temperature thermoelastic model with a memory-dependent derivative has been constructed for a two-dimensional magneto-thermoelastic problem interacting in an isotropic homogeneous, perfectly conducting semi-infinite medium under the fuzzy environment. The thermophysical fuzzy variables like displacement, temperature, and other variables are considered in r-cut form. The theoretical solutions of coupled partial differential equations are calculated in the combined Laplace–Fourier transformed domain using the eigenvalue approach under the traction-free boundary and thermal shock, which is dependent on time. Numerical results of thermophysical fuzzy variables are illustrated graphically for varying parameters such as time delay, kernel functions, and time and are compared with their respective crisp plots. The real-life applications and conclusions based on analytical and numerical results are discussed later on.