Modeling of memory-dependent derivative in generalized thermoelasticity

M. A. Ezzat; A. S. El-Karamany; A. A. El-Bary

doi:10.1140/epjp/i2016-16372-3

EPJ

Modeling of memory-dependent derivative in generalized thermoelasticity

M. A. Ezzat¹^*, A. S. El-Karamany² and A. A. El-Bary³

¹ Department of Mathematics, Faculty of Education, Alexandria University, Alexandria, Egypt
² Department of Mathematical and Physical Sciences, Nizwa University, P.O. Box 1357, 611, Nizwa, Oman
³ Arab Academy for Science and Technology, P.O. Box 1029, Alexandria, Egypt

Received: 12 May 2016
Accepted: 20 September 2016
Published online: 24 October 2016

Abstract

The generalized thermoelasticty equations based on memory-dependent derivative (MDD) is modeled so that some essential theories can be easily obtained. The exact solutions for different problems in Laplace transform domain are obtained. A numerical method is employed for the inversion of the Laplace transforms. The results are compared to those of the indicated theories of generalized thermoelasticity. The effects of the time-delay on thermoelasticity for different linear forms of Kernel functions are discussed.

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EPJ

Modeling of memory-dependent derivative in generalized thermoelasticity

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