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

• Published in: AIMS mathematics Vol. 5; no. 2; pp. 894 - 903
• Main Authors: K. Ali, Karmina, Yilmazer, Resat
• Format: Journal Article
• Language: English
• Published: AIMS Press 01.01.2020
• Subjects: discrete fractional; the effective mass schrodinger equation; the nabla operator
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.2020061

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.