A study of ∇-discrete fractional calculus operator on the radial Schrödinger equation for some physical potentials

Abstract

The fractional calculus includes concepts of integrals and derivatives of any complex or real order. The fractional calculus is as old as the usual calculus. Recently, many scientists have been studying on this field to provide the development and applicability to various areas of mathematics, physics, engineering and other sciences. The discrete fractional calculus has an important position in this field. Some ordinary diffrential equations can be solved by means of nabla (∇) discrete fractional calculus operator. In this paper, we aim to apply this operator to the radial Schrödinger equation for some physical potentials such as pseudoharmonic and Mie-type potentials.

Mathematics Subject Classification (2010):

• 26A33
• 34A08
• 39A70
• 47B39

Key words:

• Fractional calculus
• discrete fractional calculus
• ∇-discrete fractional calculus operator
• Leibniz rule
• radial Schrödinger equation