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Analogues to Lie Method and Noether’s Theorem in Fractal Calculus

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Young Researchers and Elite Club, Urmia Branch, Islamic Azad University, Urmia 57169-63896, Iran
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Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, 65080 Tuşba/Van, Turkey
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Author to whom correspondence should be addressed.
Fractal Fract 2019, 3(2), 25; https://doi.org/10.3390/fractalfract3020025
Received: 17 April 2019 / Revised: 3 May 2019 / Accepted: 6 May 2019 / Published: 7 May 2019
In this manuscript, we study symmetries of fractal differential equations. We show that using symmetry properties, one of the solutions can map to another solution. We obtain canonical coordinate systems for differential equations on fractal sets, which makes them simpler to solve. An analogue for Noether’s Theorem on fractal sets is given, and a corresponding conservative quantity is suggested. Several examples are solved to illustrate the results. View Full-Text
Keywords: staircase function; local fractal derivatives; fractal Lie symmetry; fractal Noether’s theorem; fractal Lie method staircase function; local fractal derivatives; fractal Lie symmetry; fractal Noether’s theorem; fractal Lie method
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Khalili Golmankhaneh, A.; Tunç, C. Analogues to Lie Method and Noether’s Theorem in Fractal Calculus. Fractal Fract 2019, 3, 25.

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