Modifications at large distances from fractional and fractal arguments. (English) Zbl 1196.28014
Summary: The main aim of this short communication is to consider the general fractional properties of gravitational field based on the modified generalized Kim-Srivastava left-sided Erdélyi-Kober fractional integral approach that is generated by a fractal distribution of particles. We found that the gravitational field force could be modified at large distances without the presence of extra-dimensions or any source of dark energy.
References:
| [1] | Oldham K. B., The Fractional Calculus (1974) · Zbl 0292.26011 |
| [2] | Samko S., Fractional Integrals and Derivatives: Theory and Applications (1993) |
| [3] | Miller K. S., An Introduction to the Fractional Calculus and Fractional Differential Equations (1993) · Zbl 0789.26002 |
| [4] | Podlubny I., An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications (1999) · Zbl 0924.34008 |
| [5] | DOI: 10.1142/9789812817747_0002 · doi:10.1142/9789812817747_0002 |
| [6] | DOI: 10.1007/s11071-004-3755-7 · Zbl 1142.74302 · doi:10.1007/s11071-004-3755-7 |
| [7] | DOI: 10.1007/BF01174319 · Zbl 0901.73030 · doi:10.1007/BF01174319 |
| [8] | El-Nabulsi R. A., Rom. J. Phys. 52 pp 705– |
| [9] | El-Nabulsi R. A., Rom. Rep. Phys. 59 pp 763– |
| [10] | DOI: 10.1016/j.chaos.2009.03.115 · doi:10.1016/j.chaos.2009.03.115 |
| [11] | DOI: 10.1063/1.2929662 · Zbl 1152.81422 · doi:10.1063/1.2929662 |
| [12] | DOI: 10.1002/mma.879 · Zbl 1177.49036 · doi:10.1002/mma.879 |
| [13] | El-Nabulsi R. A., Chaos Solitons Fractals 42 pp 377– |
| [14] | DOI: 10.1142/S021988780900345X · Zbl 1166.83014 · doi:10.1142/S021988780900345X |
| [15] | DOI: 10.1142/S0219887808003119 · Zbl 1172.26305 · doi:10.1142/S0219887808003119 |
| [16] | DOI: 10.1142/S0217984909021387 · Zbl 1185.81089 · doi:10.1142/S0217984909021387 |
| [17] | DOI: 10.1007/s10569-005-1152-2 · Zbl 1145.85002 · doi:10.1007/s10569-005-1152-2 |
| [18] | DOI: 10.1007/978-3-540-47582-8_4 · doi:10.1007/978-3-540-47582-8_4 |
| [19] | DOI: 10.1111/j.1365-2966.2005.09578.x · doi:10.1111/j.1365-2966.2005.09578.x |
| [20] | Connes A., Noncommutative Geometry (1994) |
| [21] | Lauscher O., J. High Energy Phys. 10 pp 50– |
| [22] | DOI: 10.1016/j.aop.2005.01.004 · Zbl 1071.76002 · doi:10.1016/j.aop.2005.01.004 |
| [23] | Kober H., Quart. J. Math. pp 193– |
| [24] | Luchko Y., Fract. Cal. Appl. Anal. 7 pp 339– |
| [25] | DOI: 10.1080/17476939708815054 · Zbl 0951.30010 · doi:10.1080/17476939708815054 |
| [26] | Raina R. K., J. Fract. Calculus 14 pp 45– |
| [27] | Colombeau J. F., New Generalized Functions and Multiplication of Distributions (1984) · Zbl 0532.46019 |
| [28] | DOI: 10.1016/j.cpc.2007.11.007 · Zbl 1196.33020 · doi:10.1016/j.cpc.2007.11.007 |
| [29] | Raina R. K., Rend. Del. Sem. Mat. Della Univ. Padova 97 pp 61– |
| [30] | DOI: 10.1080/10556790008238588 · doi:10.1080/10556790008238588 |
| [31] | Durrer R., Astron. Astrophys. Lett. 339 pp L85– |
| [32] | Mandelbrot B., The Fractal Geometry of Nature (1982) · Zbl 0504.28001 |
| [33] | Bunkin N. F., JETP Lett. 58 pp 94– |
| [34] | DOI: 10.1086/160884 · doi:10.1086/160884 |
| [35] | DOI: 10.1051/0004-6361:20065321 · doi:10.1051/0004-6361:20065321 |
| [36] | DOI: 10.1016/j.physa.2004.06.056 · doi:10.1016/j.physa.2004.06.056 |
| [37] | Sylos Labini F., Europhys. Lett. 86 pp 490010– |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
