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More specifically, a linear spectral problem associated with the KdV equation of integer order is first equipped with local time\u2010fractional derivative. Based on the spectral problem with the equipped local time\u2010fractional derivative, the local tfKdV equation with Lax integrability is then derived and solved by extending the spectral transform. As a result, a formula of exact solution with Mittag\u2010Leffler functions is obtained. Finally, in the case of reflectionless potential the obtained exact solution is reduced to fractional <jats:italic>n<\/jats:italic>\u2010soliton solution. In order to gain more insights into the fractional <jats:italic>n<\/jats:italic>\u2010soliton dynamics, the dynamical evolutions of the reduced fractional one\u2010, two\u2010, and three\u2010soliton solutions are simulated. It is shown that the velocities of the reduced fractional one\u2010, two\u2010, and three\u2010soliton solutions change with the fractional order.<\/jats:p>","DOI":"10.1155\/2019\/7952871","type":"journal-article","created":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T23:31:20Z","timestamp":1565134280000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Fractional Soliton Dynamics and Spectral Transform of Time\u2010Fractional Nonlinear Systems: A Concrete 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