General Solution to Sequential Linear Conformable Fractional Differential Equations With Constant Coefficients

TL;DR

This paper provides a comprehensive method for solving sequential linear conformable fractional differential equations with constant coefficients, extending classical solutions using fractional exponential functions and variation of parameters.

Contribution

It introduces a general solution framework for conformable fractional differential equations with constant coefficients, including homogeneous and non-homogeneous cases.

Findings

General solution using fractional exponential functions

Extension of variation of parameters to fractional equations

Applicable to both homogeneous and non-homogeneous cases

Abstract

In this work, we give the general solution sequential linear conformable fractional differential equations in the case of constant coefficients for {\alpha}(\in)(0,1]. In homogeneous case, we use a fractional exponential function which generalizes the corresponding ordinary function. In non-homogeneous case, we present to fractional the method of variation of parameters for a particular solution of sequential linear conformable fractional differential equations.