Local fractional variational iteration algorithm II for non-homogeneous model associated with the non-differentiable heat flow

Abstract

In this article, we begin with the non-homogeneous model for the non-differentiable heat flow, which is described using the local fractional vector calculus, from the first law of thermodynamics in fractal media point view. We employ the local fractional variational iteration algorithm II to solve the fractal heat equations. The obtained results show the nondifferentiable behaviors of temperature fields of fractal heat flow defined on Cantor sets. KeywordsLocal fractional variational iteration algorithm II, non-homogeneous model, heat flow, non-differentiable functions, local fractional derivative operators Date

Non-differentiable Solutions for Local Fractional Nonlinear Riccati Differential Equations

“…where ζ is the fractal dimension of the local fractional operator [1][2][3][4][5][6][7][8][9][10][11][12][13], ̟ 0 (µ) = 0 and ̟ 2 (µ) = 0. Our main aim is to study non-differentiable solutions of LFNRDE.…”

The Yang Laplace transform- DJ iteration method for solving the local fractional differential equation

“…So there are many fractional derivatives up to know. Unlike other fractional derivatives, the local fractional derivative can be dealt with the differential equations on the Cantor space, for example [6,8,9,14,16]. There are many methods for solving the local fractional differential equations, such as the integral transformation method, the two-dimensional extended differential transform approach, the variational iteration transform method, the Sumudu transform method, the local fractional homotopy perturbation method and so on (see [1, 3-5, 11-13, 15]).…”

An Intriguing Approach to The Fractional Mellin Transform Method

“…On the other side, in recent decades, non integer (fractional) differentiation has become a more and more popular tool for modeling physical systems from diverse areas such as heat flow [2], electrical circuits [3]- [5], control [6]- [8] and medicine [9]. Thus the hug of Mellin analysis and fractional analysis was inevitable and in the literature, one can find so many fractional calculus applications that use Mellin transform as a solution method [10]- [13].…”