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Fractional Derivative Cosmology
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The degree by which a function can be differentiated need not be restricted to integer values. Usually most of the field equations of physics are taken to be second order, curiosity asks what happens if this is only approximately the case and the field equations are nearly second order. For Robertson-Walker cosmology there is a simple fractional modification of the Friedman and conservation equations. In general fractional gravitational equations similar to Einstein's are hard to define as this requires fractional derivative geometry. What fractional derivative geometry might entail is briefly looked at and it turns out that even asking very simple questions in two dimensions leads to ambiguous or intractable results. A two dimensional line element which depends on the Gamma-function is looked at.
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Cited by 3 Pith papers
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An Interplay Between Fractional Calculus and Holographic Dark Energy
Introduces Fractional Holographic Dark Energy (FHDE) via fractionally corrected entropy from a modified Wheeler-DeWitt equation and studies its late-time cosmology, field reconstructions, and extensions to modified gr...
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Fractional Einstein field equations in $2+1$ dimensional spacetime
A weighted Riemann-Liouville fractional derivative is introduced; near the classical limit, the fractional Einstein equations with the BTZ metric reproduce a charged BTZ solution with an anisotropic cosmological constant.
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Gravitational Foundations and Exact Solutions in $n$-Dimensional Fractional Cosmology
A fractional-kernel Sáez–Ballester action in n dimensions yields exact FLRW solutions whose effective equation of state can reproduce all cosmic epochs for hand-chosen values of α and C.
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