Waves in fractional Zener type viscoelastic media

Journal of Mathematical Analysis and Applications

Volumn 365, Issue 1, 2010, Pages 259-268

  Konjik, Sanja ^a   Oparnica, Ljubica ^b   Zorica, Dusan ^c  

^a University of Novi Sad   (Serbia)

^b MATHEMATICAL INSTITUTE   (Serbia)

^c UNIVERSITY OF NOVI SAD   (Serbia)

Author keywords

Fractional derivatives; Fractional Zener model; Fundamental solution; Laplace and Fourier transforms

Indexed keywords

EID: 73549089905     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2009.10.043     Document Type: Article

References (21)

1. Atanackovic T.M. A modified Zener model of viscoelastic body. Contin. Mech. Thermodyn. 14 (2002) 137-148
2. Atanackovic T.M., and Guran A. Theory of Elasticity for Scientists and Engineers (2000), Birkhäuser, Boston
3. Atanackovi T.M., Pilipovic S., and Zorica D. Diffusion wave equation with two fractional derivatives of different order. J. Phys. A: Math. Gen. 40 (2007) 5319-5333
4. Atanackovic T.M., Pilipovic S., and Zorica D. Time distributed-order diffusion-wave equation. I. Volterra-type equation. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 465 (2009) 1869-1891
5. Atanackovic T.M., Pilipovic S., and Zorica D. Time distributed-order diffusion-wave equation. II. Applications of Laplace and Fourier transformations. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 465 (2009) 1893-1917
6. Caputo M., and Mainardi F. A new dissipation model based on memory mechanism. Pure Appl. Geophys. 91 (1971) 134-147
7. Caputo M., and Mainardi F. Linear models of dissipation in anelastic solids. Riv. Nuovo Cimento (Ser. II) 1 (1971) 161-198
8. Dautry R., and Lions J.L. Mathematical Analysis and Numerical Methods for Science and Technology, vol. 5 (2000), Springer-Verlag, Berlin
9. Gonsovski V.L., and A Yu. Rossikhin Stress waves in a viscoelastic medium with a singular hereditary kernel. J. Appl. Mech. Tech. Phys. 14 (1973) 595-597
10. Hanyga A. Multi-dimensional solutions of space-time-fractional diffusion equations. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 458 (2002) 429-450
11. Hanyga A. Multidimensional solutions of time-fractional diffusion-wave equations. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 458 (2002) 933-957
12. Kochubei A.N. Distributed order calculus and equations of ultraslow diffusion. J. Math. Anal. Appl. 340 (2008) 252-281
13. Mainardi F. Fractional calculus: Some basic problems in continuum and statistical mechanics. In: Mainardi F., and Carpinteri A. (Eds). Fractals and Fractional Calculus in Continuum Mechanics. CISM Courses and Lectures vol. 378 (1997), Springer-Verlag, Wien-New York 291-348
14. Mainardi F., Pagnini G., and Gorenflo R. Some aspects of fractional diffusion equations of single and distributed order. Appl. Math. Comput. 187 (2007) 295-305
15. Oparnica Lj. Generalized fractional calculus with applications in mechanics. Mat. Vesnik 53 (2002) 151-158
16. Podlubny I. Fractional Differential Equations (1999), Academic Press, San Diego
17. N Yu. Rabotnov equilibrium of an elastic medium with after effect. Prikl. Mat. Mekh. 12 (1948) 81-91 (in Russian)
18. Rossikhin Yu.A., and Shitikova M.V. A new method for solving dynamic problems of fractional derivative viscoelasticity. Internat. J. Engrg. Sci. 39 (2001) 149-176
19. Samko S.G., Kilbas A.A., and Marichev O.I. Fractional Integrals and Derivatives - Theory and Applications (1993), Gordon and Breach Science Publishers, Amsterdam
20. Treves F. Basic Linear Partial Differential Equations (1975), Academic Press, New York
21. Vladimirov V.S. Equations of Mathematical Physics (1984), Mir Publishers, Moscow