Two temperature generalized thermoelasticity involving memory-dependent derivative under fuzzy environment

• Published in: Waves in random and complex media Vol. 34; no. 4; pp. 3620 - 3635
• Main Authors: Mandal, Saroj, Middya, Monalisa, Pal (Sarkar), Smita
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 03.07.2024; Taylor & Francis Ltd
• Subjects: Derivatives; Exact solutions; Free boundaries; fuzzy approach; Fuzzy logic; Fuzzy sets; Graphical representations; Half spaces; Kernel functions; Laplace transformation; Laplace transforms; Mathematical analysis; memory-dependent derivative; Partial differential equations; Temperature dependence; Thermal shock; Thermal transformations; Thermoelasticity; Time dependence; Time domain analysis; Time lag; triangular fuzzy number; Two temperature generalised thermoelasticity; vector matrix differential equation
• ISSN: 1745-5030; 1745-5049
• DOI: 10.1080/17455030.2021.1983229

A one-dimensional two-temperature model of generalized thermoelasticity theory in half-space has been studied in this present discussion with memory-dependent derivative. The fuzzy approach has been applied to construct the governing equations. The fuzzy variables such as stress, strain and so on are represented in r-cut. The coupled partial differential equations' analytical solutions are obtained in Laplace transform domain subject to a stress-free boundary with a time-dependent imprecise thermal shock. A suitable numerical inverse Laplace transformation technique is applied to get the space time-domain results for different time delay parameter values and several kernel functions. Two examples of numerical results in the fuzzy environment are performed and are compared with the crisp results graphically. The concluding remarks are made based on numerical results and graphs.