Application of the Fractional Calculus to the Radial Schr�dinger Equation given by the Makarov Potential

O. Ozturk
Department of Mathematics,
Faculty of Arts and Sciences,
Bitlis Eren University,
13000 Bitlis, Turkey

Received 10 October, 2016; accepted in revised form 22 March, 2018

Abstract: Fractional calculus and its generalizations are used for the solutions of some classes of differential
equations and fractional differential equations. In this paper, our aim is to solve the radial Schr�dinger
equation given by the Makarov potential by the help of fractional calculus theorems. The related equation
was solved by applying a fractional calculus theorem that gives fractional solutions of the second order
differential equations with singular points. In the last section, we also introduced hypergeometric form of
this solution.

� European Society of Computational Methods in Sciences and Engineering
Keywords: Fractional calculus, Generalized Leibniz rule, Radial Schr�dinger equation, Makarov potential
Mathematics Subject Classification: 26A33, 34A08


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