×

Analytical and numerical solutions of time fractional anomalous thermal diffusion equation in composite medium. (English) Zbl 1322.80004

Summary: In this paper, we set up a time fractional thermal diffusion equation in one-dimensional composite medium. Analytical and numerical methods are proposed to solve the equation of fractional thermal diffusion in M-layers composite medium. To illustrate the effectiveness of the method,a time fractional heat flow equation of two layers is considered. Numerical results show that the proposed methods are accurate and efficient. The classical heat conduction problem in one-dimensional composite medium can be regarded as particular cases of this paper. The proposed method can be developed for different situations to calculate anomalous diffusion problems in composite medium.

MSC:

80A20 Heat and mass transfer, heat flow (MSC2010)
74E30 Composite and mixture properties
35R11 Fractional partial differential equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Metzler, Physica A 211 pp 13– (1994) · doi:10.1016/0378-4371(94)90064-7
[2] Tan, Appl. Phys. Lett. 91 pp 183901– (2007) · doi:10.1063/1.2805208
[3] Wei, Z. Angew. Math. Mech. 93 pp 14– (2011) · Zbl 1263.65098 · doi:10.1002/zamm.201200003
[4] Sandev, J. Phys. A: Math. Theor. 44 pp 255203– (2011) · Zbl 1301.82042 · doi:10.1088/1751-8113/44/25/255203
[5] Atanackovic, Z. Angew. Math. Mech. 87 pp 537– (2007) · Zbl 1131.34003 · doi:10.1002/zamm.200710335
[6] Zhuang, J. Appl. Math. Comput. 22(3) pp 87– (2006) · Zbl 1140.65094 · doi:10.1007/BF02832039
[7] Liu, J. Comput. Appl. Math. 166 pp 209– (2004) · Zbl 1036.82019 · doi:10.1016/j.cam.2003.09.028
[8] Craiem, Phys. Biol. 7 pp 013001– (2010) · doi:10.1088/1478-3975/7/1/013001
[9] Qi, Physica A 390 pp 1876– (2011) · Zbl 1225.35253 · doi:10.1016/j.physa.2011.02.010
[10] F. Khanna D. Matrasulov
[11] Li, Phys. Rev. Lett. 91 pp 044301– (2003) · doi:10.1103/PhysRevLett.91.044301
[12] Povstenko, J. Thermal Stresses 28 pp 83– (2005) · Zbl 1211.35148 · doi:10.1080/014957390523741
[13] I. Podlubny
[14] Jiang, Physica A 389 pp 3368– (2010) · doi:10.1016/j.physa.2010.04.023
[15] Singh, Math. Comput. Model. 54 pp 2316– (2011) · Zbl 1235.65113 · doi:10.1016/j.mcm.2011.05.040
[16] M.N. Özisik
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.