Solutions of Sequential Conformable Fractional Differential Equations around an Ordinary Point and Conformable Fractional Hermite Differential Equation

TL;DR

This paper develops power series solutions for variable coefficient conformable fractional differential equations of order 2α and introduces conformable fractional Hermite equations and polynomials, expanding fractional calculus tools.

Contribution

It provides the first systematic solutions around ordinary points for these fractional equations and defines new conformable fractional Hermite polynomials.

Findings

Power series solutions for variable coefficient equations derived

Introduction of conformable fractional Hermite differential equations

Properties of conformable fractional Hermite polynomials established

Abstract

In this work, we give the power series solutions around an ordinary point, in the case of variable coefficients, homogeneous sequential linear conformable fractional differential equations of order 2\alpha. Further, we introduce the conformable fractional Hermite differential equations, conformable fractional Hermite polynomials and basic properties of these polynomials.