Prof Stephen Hawking's final research paper suggests that our Universe may be one of many similar to our own. It also points a way forward for astronomers to find evidence of the existence of parallel universes. In the s, the Cambridge scientist, along with US physicist James Hartle developed a new idea about the beginning of the Universe. This resolved a difficulty with Einstein's theory that suggested that the Universe began nearly 14 billion years ago but said nothing about how it began. Instead, the Hartle-Hawking idea used a different theory called quantum mechanics to explain how the Universe arose from nothingness.
An operational matrix of fractional integration of the Laguerre polynomials and its application on a semi-infinite interval. Purpose: In this paper, we construct the operational matrix of fractional integration of arbitrary order for Laguerre polynomials. Methods: We introduce some necessary definitions and give some relevant properties of Laguerre polynomials. The fractional integration is described in the Riemann-Liouville sense. We develop a direct solution technique for solving the integrated forms of fractional differential equations FDEs on the half line using the Laguerre tau method based on operational matrix of fractional integration in the Riemann-Liouville sense.
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