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We formulate the fractional Ricci flow theory for (pseudo) Riemannian geometries enabled with nonholonomic distributions defining fractional integro-differential structures, for non-integer dimensions.
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S. Vacaru, Nonholonomic Ricci flows: II. Evolution equations and dynamics, J. Math. Phys. 49
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S. Vacaru, Finsler and Lagrange geometries in Einstein and string gravity, Int. J. Geom. Methods. Mod. Phys. (IJGMMP) 5
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V. E. Tarasov, Fractional vector calculus and fractional Maxwell’s equations, Annals of Phys. (NY) 323
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S. Vacaru, The Entropy of Lagrange–Finsler spaces and Ricci flows, Rep. Math. Phys. 63
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S. Vacaru, Nonholonomic Ricci flows, exact solutions in gravity, and symmetric and nonsymmetric metrics, Int. J. Theor. Phys. 48
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A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Application of Fractional Differential Equations (Elsevier, Amsterdam, 2006)
2006
Cited alongside, same era.
S. Vacaru, Ricci flows and solitonic pp–waves, Int. J. Mod. Phys. A 21
2006
Cited alongside, same era.
S. Vacaru, Parametric nonholonomic frame transforms and exact solutions in gravity, Int. J. Geom. Methods. Mod. Phys. (IJGMMP) 4
2007
Cited alongside, same era.
D. Baleanu and S. Muslih, On fractional variational principles, Adv. Frac. Calc. Part 2 (2007) 115–126
2007
Cited alongside, same era.
S. Vacaru and M. Visinescu, Nonholonomic Ricci flows and running cosmological constant: I. 4D Taub-NUT metrics, Int. J. Mod. Phys. A 22
2007
Cited alongside, same era.
G. Perelman, The entropy formula for the Ricci flow and its geometric applications, arXiv: math.DG/ 0211159
Cited in the paper.
G. Perelman, Ricci flow with surgery on three–manifolds, arXiv: math. DG/ 03109
Cited in the paper.
S. Vacaru, Branes and quantization for an A–model complexification of Einstein gravity in Almost Kähler variables, Int. J. Geom. Methods. Mod. Phys. (IJGMMP) 6
2009
Later among the works it cites.
S. Vacaru, Nonholonomic Ricci flows: Exact solutions and gravity, Electronic Journal of Theoretical Physics (EJTP) 6
2009
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S. Vacaru, Nonholonomic Ricci flows and parametric deformations of the solitonic pp-Waves and Schwarzschild solutions, Electronic Journal of Theoretical Physics (EJTP) 6
2009
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S. Vacaru, On general solutions in Einstein and higher dimension gravity, Int. J. Theor. Phys. 49
2010
Closest in time.
S. Vacaru, Nonholonomic Ricci flows: III. Curve flows and solitonic hierarchies, arXiv: 0704.2062
2062
Closest in time.