Discrete fractional solutions to the effective mass Schrödinger equation by mean of nabla operator

Karmina K. Ali; Resat Yilmazer; Karmina K. Ali; Resat Yilmazer

doi:10.3934/math.2020061

AIMS Mathematics

2020, Volume 5, Issue 2: 894-903. doi: 10.3934/math.2020061

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Research article

Discrete fractional solutions to the effective mass Schrödinger equation by mean of nabla operator

Karmina K. Ali ^{1,2
,
,},
Resat Yilmazer ²

1.
Faculty of Science, Department of Mathematics, University of Zakho, Iraq
2.
Faculty of Science, Department of Mathematics, Firat University, Elazig, Turkey

Received: 14 October 2019 Accepted: 02 January 2020 Published: 07 January 2020
MSC : 97M50, 97N70

In the current article, we investigate the second order singular differential equation namely the effective mass Schrödinger equation by means of the fractional nabla operator. We apply some classical transformations in order to reduce the governing equation, and also restrict the difference parameters involved in order to find them values. In order to achieve these important results, certain tools such as the Leibniz rule, the index law, the shift operator, and the power rule are provided in view of the discrete fractional calculus. We use all these mentioned data for two representations of the given model for homogeneous and non-homogeneous instances. The main advantage of the fractional nabla operator is to apply the singular differential equations and transform them into a fractional order model. As a result, we produce some new exact fractional solutions to the present model for a given potential.
- discrete fractional,
- the nabla operator,
- the effective mass Schrodinger equation
Citation: Karmina K. Ali, Resat Yilmazer. Discrete fractional solutions to the effective mass Schrödinger equation by mean of nabla operator[J]. AIMS Mathematics, 2020, 5(2): 894-903. doi: 10.3934/math.2020061

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Abstract

In the current article, we investigate the second order singular differential equation namely the effective mass Schrödinger equation by means of the fractional nabla operator. We apply some classical transformations in order to reduce the governing equation, and also restrict the difference parameters involved in order to find them values. In order to achieve these important results, certain tools such as the Leibniz rule, the index law, the shift operator, and the power rule are provided in view of the discrete fractional calculus. We use all these mentioned data for two representations of the given model for homogeneous and non-homogeneous instances. The main advantage of the fractional nabla operator is to apply the singular differential equations and transform them into a fractional order model. As a result, we produce some new exact fractional solutions to the present model for a given potential.

References

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