Fractional extensions of the temperature field problems in oil strata

Applied Mathematics and Computation

Volumn 186, Issue 1, 2007, Pages 35-44

  Galue, Leda ^a   Kalla, S L ^b   Al Saqabi, B N ^b  

^a UNIVERSIDAD DEL ZULIA   (Venezuela)

^b KUWAIT UNIVERSITY   (Kuwait)

Author keywords

Bessel functions; Fractional derivatives; Integral transforms

Indexed keywords

BESSEL FUNCTIONS; LAPLACE EQUATION; NUMERICAL METHODS; PROBLEM SOLVING; THEOREM PROVING;

FRACTIONAL DERIVATIVES; HEAT EQUATIONS; INTEGRAL TRANSFORMS; LAPLACE CONVOLUTION;

OIL WELLS;

EID: 33947198285     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2006.07.086     Document Type: Article

References (16)

1. Antimirov M.Ya., Kolyshkin A.A., and Vailancourt R. Applied Integral Transforms (1993), American Mathematical Society, Providence Rhode Island, USA
2. Ben Nakhi Y., and Kalla S.L. Some boundary value problems of temperature fields in oil strata. Appl. Math. Comput. 146 (2003) 105-119
3. Boyadjiev L., and Scherer R. Fractional extensions of the temperature field problem in oil strata. Kuwait J. Sci. Eng. 31 2 (2004) 15-32
4. Boyadjiev L., Kamenov O., and Kalla S.L. On the Lauwerier formulation of the temperature field problem in oil strata. Int. J. Math. Sci. 10 (2005) 1577-1588
5. Caputo M. Linear models of dissipation whose Q is almost frequency independent - II. Geophys. J. Roy. Astro. Soc. 13 (1967) 529-539
6. Caputo M., and Mainardi F. A new dissipation model based on memory mechanism. Pure Appl. Geophys. 91 (1971) 134-147
7. Ditkin V.A., and Prudnikov A.P. Integral Transforms and Operational Calculus (1965), Pergamon Press, New York, NY, USA
8. V.A. Ditkin, A.P. Prudnikov, Formulaire Pour le Calcul Operationnel Masson et Cie, Paris, France, 1967.
9. Kiryakova V.S. Generalized Fractional Calculus and Applications (1994), Longman, London
10. Lebedev N.N. Special Functions and Their Applications (1965), Prentice-Hall, Englewood Cliffs, NJ, USA
11. Mainardi F. The fundamental solutions for the fractional diffusion-wave equation. Appl. Math. Lett. 9 6 (1996) 23-28
12. Podlubny I. Fractional Differential Equations. An Introduction to Fractional Derivatives, Fractional Differential Equations Methods of Their Solution and some of Their Applications (1999), Academic Press, San Diego, CA, USA
13. Prudnikov A.P., Brichkov Yu., and Marichev O.I. Integrals and Series vol. 3 (1993), Gordon and Breach
14. Samko S.G., Kilbas A.A., and Marichev O.I. The Fractional Integrals and Derivatives. Theory and Applications (1993), Gordon and Breach, Amsterdam, The Netherlands
15. R. Scherer, S.L. Kalla, L. Boyadjiev, B.N. Al Saqabi, Numerical treatment of fractional heat equations, 2006.
16. Spiegel M.R. Theory and Problems of Laplace Transforms (1965), Schaum Publishing Co., New York, NY, USA