Fractional wave equation with a frictional memory kernel of Mittag-Leffler type. (English) Zbl 1246.35204
Summary: The authors give an analytical treatment of a fractional wave equation with Caputo time fractional derivative and frictional memory kernel of Mittag-Leffler type. This problem generalizes a recently solved problem [the author and T. Sandev, Comput. Math. Appl. 62, No. 3, 1554–1561 (2011; Zbl 1228.35246)] of a wave equation for a vibrating string in presence of a fractional friction with power-law memory kernel. Such equations can be used in the context of modeling processes in complex and viscoelastic media.
MSC:
| 35R11 | Fractional partial differential equations |
| 74H45 | Vibrations in dynamical problems in solid mechanics |
| 74K05 | Strings |
| 33E15 | Other wave functions |
Keywords:
fractional wave equation; memory kernel; Caputo time fractional derivative; Mittag-Leffler function; fractional integral operator; Sturm-Liouville problemCitations:
Zbl 1228.35246References:
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