Multi-fractional-differential operators for a thermo-elastic magnetic response in an unbounded solid with a spherical hole via the DPL model

AIMS Mathematics

article

Osama Moaaz¹  Ahmed E. Abouelregal² 

[1] Department of Mathematics, College of Science, Qassim University;Department of Mathematics, College of Science and Arts, Jouf University;Department of Mathematics, Faculty of Science, Mansoura University

关键词: Multi-fractional operators;    DPL model;    phase lags;    spherical hole;    moving heat flow;   

DOI  :  10.3934/math.2023282

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

The current research aims to investigate thermodynamic responses to thermal media based on a modified mathematical model in the field of thermoelasticity. In this context, it was considered to present a new model with a fractional time derivative that includes Caputo-Fabrizio and Atangana-Baleanu fractional differential operators within the framework of the two-phase delay model. The proposed mathematical model is employed to examine the problem of an unbounded material with a spherical hole experiencing a reduced moving heat flow on its inner surface. The problem is solved analytically within the modified space utilizing the Laplace transform as the solution mechanism. An arithmetic inversion of the Laplace transform was performed and presented visually and tabularly for the studied distributions. In the tables, specific comparisons are introduced to evaluate the influences of different fractional operators and thermal properties on the response of all the fields examined.

【 授权许可】

CC BY