On a Generalized Wave Equation with Fractional Dissipation in Non-Local Elasticity
Abstract
:1. Introduction
2. Mathematical Model
- is the strain measure used in [16];
- , since ;
3. Notations
4. Solutions to the Cauchy Problem (17), (18)
- withand where
- ,
5. Numerical Examples
6. Conclusions
- 1.
- We introduced a new measure of deformation, generalizing the classical one-dimensional strain. It is non-local and contains two parameters, and In the special case , it is reduced to classical or the strain measure or the generalized strain measure used in [16]. We note that a similar formalism was used in [28] in the context of classical particle mechanics, i.e., a finite number of degrees of freedom.
- 2.
- 3.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
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Atanackovic, T.M.; Djekic, D.D.; Gilic, E.; Kacapor, E. On a Generalized Wave Equation with Fractional Dissipation in Non-Local Elasticity. Mathematics 2023, 11, 3850. https://doi.org/10.3390/math11183850
Atanackovic TM, Djekic DD, Gilic E, Kacapor E. On a Generalized Wave Equation with Fractional Dissipation in Non-Local Elasticity. Mathematics. 2023; 11(18):3850. https://doi.org/10.3390/math11183850
Chicago/Turabian StyleAtanackovic, Teodor M., Diana Dolicanin Djekic, Ersin Gilic, and Enes Kacapor. 2023. "On a Generalized Wave Equation with Fractional Dissipation in Non-Local Elasticity" Mathematics 11, no. 18: 3850. https://doi.org/10.3390/math11183850
APA StyleAtanackovic, T. M., Djekic, D. D., Gilic, E., & Kacapor, E. (2023). On a Generalized Wave Equation with Fractional Dissipation in Non-Local Elasticity. Mathematics, 11(18), 3850. https://doi.org/10.3390/math11183850