Confluent Hypergeometric Equation via Fractional Calculus Approach

TL;DR

This paper introduces a fractional calculus method to derive solutions for the confluent hypergeometric equation, offering an alternative to the traditional Frobenius approach based on integer-order calculus.

Contribution

It presents a novel fractional calculus approach for solving the confluent hypergeometric equation, simplifying the solution process compared to standard methods.

Findings

Fractional calculus provides an easier way to solve the confluent hypergeometric equation.

The method offers a new perspective distinct from classical integer-order calculus.

Potential for broader application to special functions and differential equations.

Abstract

In this paper, using the theory of the so-called fractional calculus we show that it is possible to easily obtain the solutions for the confluent hypergeometric equation. Our approach is to be compared with the standard one (Frobenius) which is based on the ordinary calculus of integer order.