In this paper, a new fractional derivative involving the normalized sinc function without singular kernel is proposed. The Laplace transform is used to find the analytical solution of the anomalous heat-diffusion problems. ...

In this paper, a new numerical approach, embedding the differential transform (DT) and Laplace transform (LT), is firstly proposed. It is considered in the local fractional derivative operator for obtaining the non-differential ...

In this Letter, we propose to use the Cantor-type cylindrical-coordinate method in order to investigate a family of local fractional differential operators on Cantor sets. Some testing examples are given to illustrate the ...

In this paper, the local fractional variational iteration method is given to handle the damped wave equation and dissipative wave equation in fractal strings. The approximation solutions show that the methodology of local ...

In this manuscript, we investigated the Euler-Lagrange equations on Cantor sets within the local fractional operators. To illustrate the proposed method two examples are presented.

In the present paper we investigate the fractal boundary value problems for the Fredholm and Volterra integral equations, heat conduction and wave equations by using the local fractional decomposition method. The operator ...

This paper points out a novel local fractional variational iteration method for processing the local fractional heat conduction equation arising in fractal heat transfer.

The initial-boundary value problems for the local fractional Laplace equation, which arises in fractal electrostatics, are investigated in this article. The non-differentiable solutions with different initial and boundary ...