Theory of fractional order generalized thermoelasticity

Journal of Heat Transfer

Volumn 132, Issue 6, 2010, Pages 1-7

  Youssef, Hamdy M ^a,b  

^a Alexandria University   (Egypt)

^b UMM AL QURA UNIVERSITY   (Saudi Arabia)

Author keywords

[No Author keywords available]

Indexed keywords

ELASTIC MATERIALS; FRACTIONAL ORDER; GENERALIZED THERMO-ELASTICITY; HALF-SPACE; NEW MODEL; NEW THEORY; NUMERICAL RESULTS; STATE-SPACE TECHNIQUE; THERMOELASTICITY THEORY; UNIQUENESS THEOREM;

LAPLACE TRANSFORMS; NUMERICAL ANALYSIS; THERMOELASTICITY; WAVELET TRANSFORMS;

ELASTICITY;

EID: 77955283494     PISSN: 00221481     EISSN: 15288943     Source Type: Journal    
DOI: 10.1115/1.4000705     Document Type: Article

References (15)

1. Kimmich, R., 2002, "Strange Kinetics, "Porous media, and NMR," J. Chem. Phys., 284, pp. 243-285.
2. Podlubny, I., 1999, Fractional Differential Equations, Academic, New York.
3. Mainardi, F., and Gorenflo, R., 2000, "On Mittag-Lettler-Type Function in Fractional Evolution Processes," J. Comput. Appl. Math., 118, pp. 283-299.
4. Povstenko, Y. Z., 2004, "Fractional Heat Conductive and Associated Thermal Stress," J. Therm. Stresses, 28, pp. 83-102.
5. Fujita, Y., 1990, "Integrodifferential Equation Which Interpolates the Heat Equation and Wave Equation (I)," Osaka J. Math., 27, pp. 309-321.
6. Fujita, Y., 1990, "Integrodifferential Equation Which Interpolates the Heat Equation And Wave Equation (II)," Osaka J. Math., 27, pp. 797-804.
7. Rabotnov, Y. N., 1966, Creep of Structure Elements, Nauka, Moscow, Russia (in Russian).
8. Rossikhin, Y. A., and Shitikova, M. V., 1997, "Applications of Fractional Calculus to Dynamic Problems of Linear and Non Linear Hereditary Mechanics of Solids," Appl. Mech. Rev., 50, pp. 15-67.
9. Lord, H. W., and Shulman, Y., 1967, "A Generalized Dynamical Theory of Thermoelasticity," J. Mech. Phys. Solids, 15, pp. 299-309.
10. Kaliski, S., 1965, "Wave Equations of Thermoelasticity," Bull. Acad. Pol. Sci., Ser. Sci. Tech., 13, pp. 253-260.
11. Ignaczak, J., 1979, "Uniqueness in Generalized Thermoelasticity," J. Therm. Stresses, 2, pp. 171-175.
12. Youssef, H. M., 2005, "State-Space on Generalized Thermoelasticity for an Infinite Material With a Spherical Cavity and Variable Thermal Conductivity Subjected to Ramp-Type Heating," Journal of Canadian Applied Mathematics Quarterly (Applied Mathematics Institute), 13(4), pp. 369-388.
13. Cullen, C. G., 1972, Matrices and Linear Transformations, 2nd ed., Addison-Wesley, Reading, MA.
14. Honig, G., and Hirdes, U., 1984, "A Method for the Numerical Inversion of Laplace Transform," J. Comput. Appl. Math., 10, pp. 113-132.
15. Youssef, H. M., 2006, "Two-Dimensional Generalized Thermoelasticity Problem for a Half-Space Subjected to Ramp-Type Heating," Eur. J. Mech. A/Solids, 25, pp. 745-763.