Diffusion problems on fractional nonlocal media

• Autorzy: Alberto Sapora , Pietro Cornetti , Alberto Carpinteri
• Języki publikacji: EN

Abstrakty

EN

In this paper, the nonlocal diffusion in one-dimensional continua is investigated by means of a fractional calculus approach. The problem is set on finite spatial domains and it is faced numerically by means of fractional finite differences, both for what concerns the transient and the steady-state regimes. Nonlinear deviations from classical solutions are observed. Furthermore, it is shown that fractional operators possess a clear physical-mechanical meaning, representing conductors, whose conductance decays as a power-law of the distance, connecting non-adjacent points of the body.

Słowa kluczowe

EN

nonlocal media; fractional calculus; heat conduction

• Czasopismo: Open Physics
• Rocznik: 2013
• Tom: 11
• Numer: 10
• Strony: 1255-1261

Daty

wydano

2013-10-01

online

2013-12-19

Twórcy

autor

Alberto Sapora

• Department of Structural, Geotechnical and Building Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Torino, Italy,

autor

Pietro Cornetti

• Department of Structural, Geotechnical and Building Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Torino, Italy,

autor

Alberto Carpinteri

• Department of Structural, Geotechnical and Building Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Torino, Italy,

Bibliografia

• [1] A. C. Eringen, D.G.B Edelen, Int. J. Eng. Sci. 10, 233 (1972) http://dx.doi.org/10.1016/0020-7225(72)90039-0[Crossref]
• [2] M. Lazar, G. A. Maugin, E. C. Aifantis. Int. J. Sol. Struct. 43, 1404 (2006) http://dx.doi.org/10.1016/j.ijsolstr.2005.04.027[Crossref]
• [3] M. Di Paola, M. Zingales, Int. J. Sol. Struct. 45, 5642 (2008) http://dx.doi.org/10.1016/j.ijsolstr.2008.06.004[Crossref]
• [4] A. Carpinteri, P. Cornetti, A. Sapora, Eur. Phys. J. Special Topics. 193, 193 (2011) http://dx.doi.org/10.1140/epjst/e2011-01391-5[Crossref]
• [5] V. E. Tarasov, G.M. Zaslavsky, Commun. Nonlinear Sci. Numer. Simul. 11, 885 (2006) http://dx.doi.org/10.1016/j.cnsns.2006.03.005[Crossref]
• [6] T. Gorenflo, F. Mainardi, J. Comput. Appl. Math. 229, 400 (2009) http://dx.doi.org/10.1016/j.cam.2008.04.005[Crossref]
• [7] T. M. Atanackovic, B. Stankovic, Acta Mech. 208, 1 (2009) http://dx.doi.org/10.1007/s00707-008-0120-9[Crossref]
• [8] T. M. Michelitsch, G.A. Maugin, M. Rahman, S. Derogar, A.F. Nowakowski, F.C.G.A. Nicolleau, J. Appl. Math. 23, 709 (2012)
• [9] A. Sapora, P. Cornetti, A. Carpinteri, Commun. Nonlinear Sci. Numer. Simulat. 18, 63 (2013) http://dx.doi.org/10.1016/j.cnsns.2012.06.017[Crossref]
• [10] N. Challamel, D. Zoricab, T.M. Atanackovic, D. T. Spasic, C. R. Mecanique 341, 298 (2013) http://dx.doi.org/10.1016/j.crme.2012.11.013[Crossref]
• [11] A. Carpinteri, P. Cornetti, A. Sapora, M. Di Paola, M. Zingales in Proceedings of the XIX Italian Conference on Theoretical and Applied Mechanics, Ancona, Italy, 2009 Ed. S. Lenci (Aras Edizioni, Fano/Italy, 2009), p.315.
• [12] M. Bogoya, C. A. Gómez, Nonlinear Analysis. 75, 3198 (2012) http://dx.doi.org/10.1016/j.na.2011.12.019[Crossref]
• [13] A. Zoia, A. Rosso, M. Kardar, Phys. Rev. E. 76, 021116 (2007) http://dx.doi.org/10.1103/PhysRevE.76.021116[Crossref]
• [14] R. Metzler, T.F. Nonnenmacher, Chem. Phys. 284, 67 (2002) http://dx.doi.org/10.1016/S0301-0104(02)00537-2[Crossref]
• [15] R. Gorenflo, F. Mainardi, D. Moretti, G. Pagnini, P. Paradisi, Chem. Phys. 284, 521 (2002) http://dx.doi.org/10.1016/S0301-0104(02)00714-0[Crossref]
• [16] R. Gorenflo, F. Mainardi, Journal of Computational and Applied Mathematics 229, 400 (2009) http://dx.doi.org/10.1016/j.cam.2008.04.005[Crossref]
• [17] P. A. Alemany, Chaos Soliton. Fract. 6, 7 (1995) http://dx.doi.org/10.1016/0960-0779(95)80003-Y[Crossref]
• [18] F. Mainardi, Chaos Soliton. Fract. 7, 1461 (1996) http://dx.doi.org/10.1016/0960-0779(95)00125-5[Crossref]
• [19] Q. Zeng, H. Li, and D. Liu, Commun. Nonlinear Sci. Numer. Simul. 4, 99 (1999) http://dx.doi.org/10.1016/S1007-5704(99)90019-9[Crossref]
• [20] F. Mainardi, Y. Luchko, G. Pagnini, Fractional Calculus Appl. Anal. 4, 153 (2001)
• [21] R. L. Magin, O. Abdullah, D. Baleanu, X. J. Zhou, J. Magn. Reson. 190, 255 (2008) http://dx.doi.org/10.1016/j.jmr.2007.11.007[Crossref]
• [22] S. Bhalekar, V. Daftardar-Gejji, D. Baleanu, R. Magin, Computers and Mathematics with Applications 61, 1355 (2011) http://dx.doi.org/10.1016/j.camwa.2010.12.079[Crossref]
• [23] S. Bhalekar, V. Daftardar-Gejji, D. Baleanu, R. Magin, Int. J. Bifurcat. Chaos 22, 1250071 (2012) http://dx.doi.org/10.1142/S021812741250071X[Crossref]
• [24] E. K. Lenzi, L. R. Evangelista and G. Barbero, J. Phys. Chem. B 113, 11371 (2009) http://dx.doi.org/10.1021/jp904741m[Crossref]
• [25] J. R. Macdonald, L. R. Evangelista, E. K. Lenzi, and G. Barbero, J. Phys. Chem. C 115, 7648 (2011) http://dx.doi.org/10.1021/jp200737z[Crossref]
• [26] O. P. Agrawal, J. Phys. A. 40, 6287 (2007) http://dx.doi.org/10.1088/1751-8113/40/24/003[Crossref]
• [27] A. Carpinteri, F. Mainardi, Fractals and Fractional Calculus in Continuum Mechanics (Springer-Verlag, Wien, 1997)
• [28] A. Carpinteri, P. Cornetti, A. Sapora, Z. Angew. Math. Mech. 89, 207 (2009) http://dx.doi.org/10.1002/zamm.200800115[Crossref]
• [29] A. Carpinteri, A. Sapora, Z. Angew. Math. Mech. 90, 203 (2010) http://dx.doi.org/10.1002/zamm.200900376[Crossref]
• [30] I. Podlubny, Fractional Differential Equations (New York, Academic Press, 1999)
• [31] M. M. Meerschaert, H. P. Scheffler, C. Tadjeran. J. Comput. Phys. 211, 249 (2006) http://dx.doi.org/10.1016/j.jcp.2005.05.017[Crossref]
• [32] M. D. Ortigueira, J. Vib. Control. 14, 1255 (2008) http://dx.doi.org/10.1177/1077546307087453[Crossref]
• [33] Q. Yang, F. Liu, I. Turner, Appl. Math. Model. 34, 200 (2010) http://dx.doi.org/10.1016/j.apm.2009.04.006[Crossref]
• [34] K. B. Oldham, J. Spanier, The Fractional Calculus (Academic Press, New York, 1974)
• [35] A. A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations (Elsevier, Amsterdam, 2006).
• [36] S. G. Samko, A. Kilbas, O.I. Marichev, Fractional Integrals and Derivatives (Gordon and Breach Science Publisher, Amsterdam, 1993)

Identyfikatory

DOI

10.2478/s11534-013-0323-0