Fetching the paper…
Reading the bibliography…
A review of different approaches to describe anisotropic fractal media is proposed.
P. Moon, D.E. Spencer, ”The meaning of the vector Laplacian”, Journal of The Franklin Institute. Vol.256. No.6. (1953) 551-558
1953
Earlier work this paper cites.
H. Joumaa, M. Ostoja-Starzewski, ”Acoustic-elastodynamic interaction in isotropic fractal media”, European Physical Journal. Special Topics. Vol.222. No.8. (2013) 1951-1960
1960
Earlier work this paper cites.
L.S. Lucena, L.R. da Silva, A.A. Tateishi, M.K. Lenzi, H.V. Ribeiro, E.K. Lenzi, ”Solutions for a fractional diffusion equation with noninteger dimensions”, Nonlinear Analysis: Real World Applications. Vol.13. No.4. (2012) 1955-1960
1960
Earlier work this paper cites.
G. ’t Hooft, M. Veltman, ”Regularization and renormalization of gauge fields”, Nuclear Physics B. Vol.44. No.1. (1972) 189-213
1972
Earlier work this paper cites.
K.G. Wilson, M.E. Fisher, ”Critical exponents in 3.99 dimensions”, Physical Review Letters. Vol.28. No.4. (1972) 240-243
1972
Earlier work this paper cites.
K.G. Wilson, ”Quantum field - theory models in less than 4 dimensions”, Physical Review D. Vol.7. No.10. (1973) 2911-2926
1973
Earlier work this paper cites.
K.G. Wilson, J. Kogut, ”The renormalization group and the ϵ \epsilon expansion”, Physics Reports. Vol.12. No.2. (1974) 75-199
1974
Earlier work this paper cites.
G. Leibbrandt, ”Introduction to the technique of dimensional regularization”, Reviews of Modern Physics. Vol.47. No.4. (1975) 849-876
1975
Earlier work this paper cites.
F.H. Stillinger, ”Axiomatic basis for spaces with noninteger dimensions”, Journal of Mathematical Physics. Vol.18. No.6. (1977) 1224-1234
1977
Earlier work this paper cites.
J.C. Collins, Renormalization
1984
Earlier work this paper cites.
K.F. Falconer, The Geometry of Fractal Sets
1985
Earlier work this paper cites.
K. Svozil, ”Quantum field theory on fractal spacetime: a new regularization method”, Journal of Physics A. Vol.20. (1987) 3861-3875
1987
Earlier work this paper cites.
J. Feder, Fractals
1988
Earlier work this paper cites.
Xing-Fei He, ”Anisotropy and isotropy: A model of fraction-dimensional space”, Solid State Communications. Vol.75. No.2. (1990) 111-114
1990
Earlier work this paper cites.
Xing-Fei He, ”Fractional dimensionality and fractional derivative spectra of interband optical transitions”, Physical Review B. Vol.42. No.18. (1990) 11751-11756
1990
Earlier work this paper cites.
A. Carpinteri, F. Mainardi (Eds.), Fractals and Fractional Calculus in Continuum Mechanics
1997
Earlier work this paper cites.
Xing-Fei He, ”Interband critical-point line shapes in confined semiconductor structures with arbitrary dimensionality: inhomogeneous broadening”, Journal of the Optical Society of America B. Vol.14. No.1. (1997) 17-20
1997
Earlier work this paper cites.
A. Thilagam, ”Stark shifts of excitonic complexes in quantum wells”, Physical Review B. Vol.56. No.8. (1997) 4665-4670
1997
Earlier work this paper cites.
A. Thilagam, ”Exciton-phonon interaction in fractional dimensional space”, Physical Review B. Vol.56. No.15. (1997) 9798-9804
1997
Earlier work this paper cites.
M. de Dios-Leyva, A. Bruno-Alfonso, A. Matos-Abiague, L.E. Oliveira, ”Fractional-dimensional space and applications in quantum-confined semiconducting heterostructures”, Journal of Applied Physics. Vol.82. No.6. (1997) 3155-3157
1997
Earlier work this paper cites.
R.S. Strichartz, ”Analysis on fractals”, Notices of the American Mathematical Society. Vol.46. No.10. (1999) 1199-1208
1999
Earlier work this paper cites.
J. Harrison, ”Flux across nonsmooth boundaries and fractal Gauss/Green/Stokes’ theorems”, Journal of Physics A. Vol.32. No.28. (1999) 5317-5328
1999
Earlier work this paper cites.
A. Thilagam, ”Pauli blocking effects in quantum wells”, Physical Review B. Vol.59. No.4. (1999) 3027-3032
1999
Earlier work this paper cites.
A. Matos-Abiague, ”Fractional dimensional momentum operator for a system of one degree of freedom”, Physica Scripta. Vol.62. No.2-3. (2000) 106-107
2000
Earlier work this paper cites.
A. Matos-Abiague, ”Free particle in fractional-dimensional space”, Bulgarian Journal of Physics. Vol.27. No.3. (2000) 54-57
2000
Earlier work this paper cites.
J. Kugami, Analysis on Fractals
2001
Earlier work this paper cites.
A. Carpinteri, B. Chiaia, P. Cornetti, ”Static-kinematic duality and the principle of virtual work in the mechanics of fractal media”, Computer Methods in Applied Mechanics and Engineering. Vol.191. No.1-2. (2001) 3-19
2001
Earlier work this paper cites.
A. Matos-Abiague, ”Deformation of quantum mechanics in fractional-dimensional space”, Journal of Physics A. Vol.34. No.49 (2001) 11059-11068. (arXiv:quant-ph/0107062)
2001
Earlier work this paper cites.
A. Matos-Abiague, ”Bose-like oscillator in fractional-dimensional space”, Journal of Physics A. Vol.34. No.14. (2001) 3125-3138
2001
Earlier work this paper cites.
A. Carpinteri, P. Cornetti, ”A fractional calculus approach to the description of stress and strain localization in fractal media”, Chaos, Solitons and Fractals. Vol.13. No.1. (2002) 85-94
2002
Earlier work this paper cites.
A. Matos-Abiague, ”Fractional-dimensional space approach for parabolic-confined polarons”, Semiconductor Science and Technology. Vol.17. No.2. (2002) 150-155
2002
Earlier work this paper cites.
A. Matos-Abiague, ”A fractional-dimensional space approach to the polaron effect in quantum wells”, Journal of Physics. Condensed Matter. Vol.14. No.17. (2002) 4543-4552
2002
Earlier work this paper cites.
A. Matos-Abiague, ”Polaron effect in G a A s − G a 1 − x A l x A s GaAs-Ga_{1-x}Al_{x}As quantum wells: A fractional-dimensional space approach”, Physical Review B. Vol.65. No.16. (2002) 165321. 9 pages
2002
Earlier work this paper cites.
A.P. Prudnikov, Yu.A. Brychkov, O.I. Marichev, Integrals and Series
2002
Earlier work this paper cites.
A. Carpinteri, B. Chiaia, P. Cornetti, ”On the mechanics of quasi-brittle materials with a fractal microstructure”, Engineering Fracture Mechanics. Vol.70. No.15. (2003) 2321-2349
2003
Earlier work this paper cites.
A. Carpinteri, P. Cornetti, K. M. Kolwankar, ”Calculation of the tensile and flexural strength of disordered materials using fractional calculus”, Chaos, Solitons and Fractals. Vol.21. No.3. (2004) 623-632
2004
Cited alongside, same era.
A. Carpinteri, B. Chiaia, P. Cornetti, ”A fractal theory for the mechanics of elastic materials”, Materials Science and Engineering A. Vol.365. No.1-2. (2004) 235-240
2004
Cited alongside, same era.
A. Carpinteri, B. Chiaia, P. Cornetti, ”A disordered microstructure material model based on fractal geometry and fractional calculus”, Zeitschrift für Angewandte Mathematik und Mechanik. Vol.84. No.2. (2004) 128-135
2004
Cited alongside, same era.
A. Carpinteri, B. Chiaia, P. Cornetti, ”The elastic problem for fractal media: Basic theory and finite element formulation”, Computer and Structures. Vol.82. No.6. (2004) 499-508
2004
Cited alongside, same era.
M. Ostoja-Starzewski, J. Li, ”Fractal materials, beams and fracture mechanics”, Zeitschrift für Angewandte Mathematik und Physik. (Journal of Applied Mathematics and Physics). Vol.60. No.6. (2009) 1194-1205
2009
Later among the works it cites.
S.I. Muslih, O.P. Agrawal, ”A scaling method and its applications to problems in fractional dimensional space”, Journal of Mathematical Physics. Vol.50. No.12. (2009) 123501. 11 pages
2009
Later among the works it cites.
R. Eid, S.I. Muslih, D. Baleanu, E. Rabei, ”On fractional Schrödinger equation in α \alpha -dimensional fractional space”, Nonlinear Analysis: Real World Applications. Vol.10. No.3. (2009) 1299-1304
2009
Later among the works it cites.
M. Sadallah, S.I. Muslih, ”Solution of the equations of motion for Einstein’s field in fractional D dimensional space-time”, International Journal of Theoretical Physics. Vol.48. No.12. (2009) 3312-3318
2009
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
A. Carpinteri, B. Chiaia, P. Cornetti, ”Numerical modelization of disordered media via fractional calculus”, Computational Material Science. Vol.30. No.1-2. (2004) 155-162
2004
Cited alongside, same era.
V.E. Tarasov, ”Fractional generalization of Liouville equations”, Chaos. Vol.14. No.1. (2004) 123-127. (arXiv:nlin.CD/0312044)
2004
Cited alongside, same era.
C. Palmer, P.N. Stavrinou, ”Equations of motion in a non-integer-dimensional space”, Journal of Physics A. Vol.37. No.27. (2004) 6987-7003
2004
Cited alongside, same era.
M.A. Lohe, A. Thilagam, ”Quantum mechanical models in fractional dimensions”, Journal of Physics A. Vol.37. No.23. (2004) 461-484
2004
Cited alongside, same era.
V.E. Tarasov, ”Continuous medium model for fractal media”, Physics Letters A. Vol.336. N.2-3. (2005) 167-174. (arXiv:cond-mat/0506137)
2005
Cited alongside, same era.
V.E. Tarasov, ”Fractional hydrodynamic equations for fractal media”, Annals of Physics. Vol.318. No.2. (2005) 286-307. (arXiv:physics/0602096)
2005
Cited alongside, same era.
V.E. Tarasov, ”Possible experimental test of continuous medium model for fractal media”, Physics Letters A. Vol.341. No.5/6. (2005) 467-472. (arXiv:physics/0602121)
2005
Cited alongside, same era.
2005
Cited alongside, same era.
2010
Later among the works it cites.
D. Baleanu, A.K. Golmankhaneh, A.K. Golmankhaneh, ”On electromagnetic field in fractional space”, Nonlinear Analysis Real World Applications. Vol.11. No.1. (2010) 288-292
2010
Later among the works it cites.
S.I. Muslih, M. Saddallah, D. Baleanu, E. Rabei, ”Lagrangian formulation of Maxwell’s field in fractional D dimensional space-time”, Romanian Reports of Physics. Vol.55. No.7-8. (2010) 659-663
2010
Later among the works it cites.
M. Zubair, M.J. Mughal, Q.A. Naqvi, ”The wave equation and general plane wave solutions in fractional space”, Progress in Electromagnetics Research Letters. Vol.19. (2010) 137-146
2010
Later among the works it cites.
V.E. Tarasov, Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media
2011
Later among the works it cites.
J. Li, M. Ostoja-Starzewski, ”Fractal solids, product measures and fractional wave equations”, Proceedings of the Royal Society A. Vol.465. No.2108. (2009) 2521-2536; and J. Li, M. Ostoja-Starzewski, ”Correction to Li and Ostoja-Starzewski 465 (2108) 2521”, Proceedings of the Royal Society A. Vol.467. No.2128. (2011) 1214. (1 page)
2011
Later among the works it cites.
P.N. Demmie, M. Ostoja-Starzewski, ”Waves in fractal media”, Journal of Elasticity. Vol.104. No.1-2. (2011) 187-204
2011
Later among the works it cites.
J. Li, M. Ostoja-Starzewski, ”Micropolar continuum mechanics of fractal media”, International Journal of Engineering Science. Vol.49. No.12. (2011) 1302-1310
2011
Later among the works it cites.
2011
Later among the works it cites.
M. Zubair, M.J. Mughal, Q.A. Naqvi, ”On electromagnetic wave propagation in fractional space”, Nonlinear Analysis: Real World Applications. Vol.12. No.5. (2011) 2844-2850
2011
Later among the works it cites.
M. Zubair, M.J. Mughal, Q.A. Naqvi, ”An exact solution of the spherical wave equation in D-dimensional fractional space”, Journal of Electromagnetic Waves and Applications. Vol.25. No.10. (2011) 1481-1491
2011
Later among the works it cites.
M. Zubair, M.J. Mughal, Q.A. Naqvi, ”An exact solution of cylindrical wave equation for electromagnetic field in fractional dimensional space”, Progress In Electromagnetics Research. Vol.114. (2011) 443-455
2011
Later among the works it cites.
2012
Later among the works it cites.
2012
Later among the works it cites.
2012
Later among the works it cites.
2012
Later among the works it cites.
2012
Later among the works it cites.
2012
Later among the works it cites.
S.I. Muslih, O.P. Agrawal, ”Schrödinger equation in fractional space”, in Fractional Dynamics and Control
2012
Later among the works it cites.
M. Zubair, M.J. Mughal, Q.A. Naqvi, Electromagnetic Fields and Waves in Fractional Dimensional Space
2012
Later among the works it cites.
2013
Later among the works it cites.
2013
Later among the works it cites.
2013
Later among the works it cites.
2013
Later among the works it cites.
T. Sandev, I. Petreska, E.K. Lenzi, ”Harmonic and anharmonic quantum-mechanical oscillators in noninteger dimensions”, Physics Letters A. Vol.378. No.3. (2013) 109-116
2013
Later among the works it cites.
M. Ostoja-Starzewski, J. Li, H. Joumaa, P.N. Demmie, ”From fractal media to continuum mechanics”, Zeitschrift für Angewandte Mathematik und Mechanik. (Journal of Applied Mathematics and Mechanics). Vol.94. No.5. (2014) 373-401
2014
Later among the works it cites.
V.E. Tarasov, ”Flow of Fractal Fluid in Pipes: Non-Integer Dimensional Space Approach”, Chaos, Solitons and Fractals. Vol.67. (2014) 26-37
2014
Later among the works it cites.
2015
Closest in time.
2053
Closest in time.
Xing-Fei He, ”Excitons in anisotropic solids: The model of fractional-dimensional space”, Physical Review B. Vol.43. No.3. (1991) 2063-2069
2069
Closest in time.