Interpolating Discrete Functions through Riemann-Liouville Fractional Integrals

Key Points

• The aim is to develop a method for interpolating functions that pass through discrete points using fractional calculus.
• Introduced a formula leveraging the Riemann-Liouville fractional derivative to extend traditional interpolation methods.
• Proved analyticity for the resulting functions derived from the interpolation process.
• Addressed generalizations for various countable sets of points under appropriate conditions.
• Established a straightforward formula for interpolating arbitrary sets of points (n, f(n)).
• Demonstrated that the interpolation method can evaluate derivatives of fractional orders in a complex plane.
• Provided conditions under which the method can be extended to different countable sets.