Solution of Homogeneous Linear Fractional Differential Equations Involving Conformable Fractional Derivative

Abstract

In this paper, we have found the solution of linear sequential fractional differential equations involving conformable fractional derivatives of order  with constant coefficients. For this purpose, we first discussed fundamental properties of the conformable derivative and then obtained successive conformable derivatives of the fractional exponential function. After this, we determined the analytic solution of linear sequential fractional differential equations (L.S.F.D.E.) in terms of a fractional exponential function. We have demonstrated this developed method with a few examples of homogeneous linear fractional differential equations. This method gives a conjugation with the method to solve classical linear differential equations with constant coefficients.