Local fractional Elzaki transform and its application to local fractional differential equations

Abstract

The objective of our work is to couple the Elzaki transform method and the local fractional derivative which is called local fractional Elzaki transform, where we have provided important results of this transformation as local fractional Laplace-Elzaki duality, Elzaki transform of the local fractional derivative and the local fractional integral and the local fractional convolution, also we have presented the properties of some special functions with the local fractional derivative sense. The Elzaki transform was applied to solve some linear local fractional differential equations in order to obtain non-differentiable analytical solutions. The results of the solved examples show the effectiveness of the proposed method.