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Keywords = Sonine–Letnikov fractional derivative

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16 pages, 297 KiB  
Article
Fractional Calculus in Russia at the End of XIX Century
by Sergei Rogosin and Maryna Dubatovskaya
Mathematics 2021, 9(15), 1736; https://doi.org/10.3390/math9151736 - 22 Jul 2021
Cited by 15 | Viewed by 2667
Abstract
In this survey paper, we analyze the development of Fractional Calculus in Russia at the end of the XIX century, in particular, the results by A. V. Letnikov, N. Ya. Sonine, and P. A. Nekrasov. Some of the discussed results are either unknown [...] Read more.
In this survey paper, we analyze the development of Fractional Calculus in Russia at the end of the XIX century, in particular, the results by A. V. Letnikov, N. Ya. Sonine, and P. A. Nekrasov. Some of the discussed results are either unknown or inaccessible. Full article
(This article belongs to the Special Issue Special Functions with Applications to Mathematical Physics)
10 pages, 249 KiB  
Article
An Application of the Sonine–Letnikov Fractional Derivative for the Radial Schrödinger Equation
by Okkes Ozturk and Resat Yilmazer
Fractal Fract. 2019, 3(2), 16; https://doi.org/10.3390/fractalfract3020016 - 4 Apr 2019
Cited by 2 | Viewed by 2716
Abstract
The Sonine–Letnikov fractional derivative provides the generalized Leibniz rule and, some singular differential equations with integer order can be transformed into the fractional differential equations. The solutions of these equations obtained by some transformations have the fractional forms, and these forms can be [...] Read more.
The Sonine–Letnikov fractional derivative provides the generalized Leibniz rule and, some singular differential equations with integer order can be transformed into the fractional differential equations. The solutions of these equations obtained by some transformations have the fractional forms, and these forms can be obtained as the explicit solutions of these singular equations by using the fractional calculus definitions of Riemann–Liouville, Grünwald–Letnikov, Caputo, etc. Explicit solutions of the Schrödinger equation have an important position in quantum mechanics due to the fact that the wave function includes all essential information for the exact definition of a physical system. In this paper, our aim is to obtain fractional solutions of the radial Schrödinger equation which is a singular differential equation with second-order, via the Sonine–Letnikov fractional derivative. Full article
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