A Different Solution Method for the Confluent Hypergeometric Equation

Abstract

Fractional calculus theory includes definition of the derivatives and integrals of arbitrary order. This theory is used to solve some classes of singular differential equations and fractional order differential equations. One of these equations is the confluent hypergeometric equation. In this paper, we intend to solve this equation by applying

Calculation of a Class of Confluent Hypergeometric Equation and Analysis of its Roles in Option Pricing Models

“…[6] acquired new generalized entropies by using the confluent hypergeometric function of the first type. Okkes [7] used fractional calculus theory to solve some classes of singular differential equations and fractional order differential equations. [8] obtained the particular solutions of the confluent hypergeometric equation by using the nabla fractional calculus operator.…”

“…The task now is to determine the coefficient, 𝑎 𝑘 such that the power series (7) satisfies the given equation and ensures that the series actually converges. If we can show that the series does converge for |𝑧 − 𝑧 0 | < 𝑟 ; 𝑟 > 0, then all the formal procedure such as differentiation term by term can be justified, and we would have constructed a solution of equation ( 6) that is valid for |𝑧 − 𝑧 0 | < 𝑟.…”