Fractional Differential Equation using Fractional order Laplace-Carson Transform

Abstract

In this paper, author have used fractional order Laplace-Carson transform to obtain solution of fractional order differential equation. The existence of α-order fractional integral transform is proved and its properties are given with proof. The fractional transform of Riemann-Liouville fractional derivative and Caputo fractional derivative is obtained using α-order fractional integral transform. Author has found specific restriction on α to solve fractional differential equation of order α using α-Laplace Carson transform.