Generalization of fractional Laplace transform for higher order and its application

Abstract

In this paper, we first introduce the conformable fractional Laplace transform. Then, we give its generalization for higher-order. Finally, as an application, we solve a non-homogeneous conformable fractional differential equation with variable coefficients and a system of fractional differential equations.

The Sequential Conformable Langevin-Type Differential Equations and Their Applications to the RLC Electric Circuit Problems

“…Theorem 2 (see [34]). Suppose f t , D α 0 f t , D 2α 0 f t ,..., D n−1 α 0 f t are continuous and D nα 0 f t is piecewise continuous on any interval 0, T .…”

Existence and Uniqueness Study of the Conformable Laplace Transform

“…Finally, as an application, we solve a non-homogeneous fractional di erential equation with variable coe cients using the conformable Laplace transform. For further results on conformable Laplace transform, see [16][17][18][19][20].…”

“…Let y: [0, ∞) ⟶ R be a continuous real-valued differentiable function and 0 < c ≤ 1. en,L c D c y(t) 􏼈 􏼉 � ζy c (ζ) − y(0), ζ > 0. (28)Theorem 10 (see[20]). Let y: [0, ∞) ⟶ R be a continuous real-valued differentiable function and 0 < c ≤ 1. en,L c D (2c) y(t) 􏽮 􏽯 � ζ 2 y c (ζ) − y (c) (0) − ζy(0), ζ > 0.…”