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We suggest a generalization of vector calculus for the case of non-integer dimensional space.
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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
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M.A. Lohe, A. Thilagam, ”Weyl-ordered polynomials in fractional-dimensional quantum mechanics”, Journal of Physics A. Vol.38. No.2. (2005) 461-484
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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
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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
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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
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V.E. Tarasov, Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media
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P.N. Demmie, M. Ostoja-Starzewski, ”Waves in fractal media”, Journal of Elasticity. Vol.104. No.1-2. (2011) 187-204
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J. Li, M. Ostoja-Starzewski, ”Micropolar continuum mechanics of fractal media”, International Journal of Engineering Science. Vol.49. No.12. (2011) 1302-1310
2011
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S.I. Muslih, O.P. Agrawal, ”Schrodinger equation in fractional space”, in Chapter 17 in ”Fractional Dynamics and Control”, (Springer, New York, 2012) 209-215
2012
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2012
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J. Martins, H.V. Ribeiro, L.R. Evangelista, L.R. da Silva, E.K. Lenzi, ”Fractional Schrodinger equation with noninteger dimensions”, Applied Mathematics and Computation. Vol.219. No.4. (2012) 2313-2319
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2012
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2012
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M. Zubair, M.J. Mughal, Q.A. Naqvi, Electromagnetic Fields and Waves in Fractional Dimensional Space
2012
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2012
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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
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2013
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D. Valerio, J.J. Trujillo, M. Rivero, J.A. Tenreiro Machado, D. Baleanu, ”Fractional calculus: A survey of useful formulas”, The European Physical Journal. Special Topics. Vol.222. No.8. (2013) 1827-1846
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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
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Xing-Fei He, ”Excitons in anisotropic solids: The model of fractional-dimensional space”, Physical Review B. Vol.43. No.3. (1991) 2063-2069
2069
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