# Approximate Solutions For Local Fractional Linear Transport Equations Arising In Fractal Porous Media

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### NEW SOLUTIONS OF THE TRANSPORT EQUATIONS IN POROUS MEDIA

6 New solutions of the transport equations in porous media within local fractional derivative 235 and its plot is depicted in Fig. 3. 0 0.2 0.4 0.6 0.8 1 0.5 1 2 4 6 8 10 t x u(x,t) Fig. 3 The non-differentiable solution of (1) with initial value (37) when α=ln2/ln3. Example 5. Let us choose the initial value of (31) given by ux E x(,0 1

### Journal Of Fractional Calculus And Applications

soil science and geomechanics. The models are primarily fractional partial differential equations (fPDEs), and in limited cases, fractional differential equations (fDEs). It develops and applies relevant fPDEs and fDEs mainly to water flow and solute transport in porous media and overland, and in some cases, to concurrent flow and energy transfer.

### VOLUME 37 NUMBER 2 MARCH 2021 Numerical Methods for Partial

EDITORS EMERITUS Mark Ainsworth Brown University Álvaro A. Aldama, Ph.D. National University of Mexico Myron B. Allen University of Wyoming Ivo Babuska

### Initial boundary value problem for fractal heat equation in

transport of thermal energy  in fractal media, the boundary value problems are described by fractional diffusion equations [16,17] solved numerically or analytically [18-21]. Moreover, especially in the case of heat conduction, this leads to non-differentiable transport

### Approximate Solutions for Local Fractional Linear Transport

ResearchArticle Approximate Solutions for Local Fractional Linear Transport Equations Arising in Fractal Porous Media MengLi,1 Xiao-FengHui,1 CarloCattani,2 Xiao-JunYang,3 andYangZhao4,5

### An efﬁcient computational technique for local fractional heat

4. Non-differential solutions for local fractional heat-conduction equations In this section, we obtain the non-differential solutions for the linear heat conduction equations by using the combination of the LFHPM and local fractional ST operator. Example 4.1. We consider the following linear local fractional heat conduction equation associated

### APPROXIMATE ANALYTIC SOLUTION OF THE FRACTAL KLEIN-GORDON

fractal Harry Dym equations was proposed in , a fractal derivative model for a porous structure was discussed , and a physical insight into a local fractional KdV-Burgers-Kuramoto (KBK

### Research Article Approximate Solutions for Local Fractional

Approximate Solutions for Local Fractional Linear Transport Equations Arising in Fractal Porous Media MengLi, 1 Xiao-FengHui, 1 CarloCattani, 2 Xiao-JunYang, 3 andYangZhao 4,5 School of Management, Harbin Institute of Technology, Harbin , China Department of Mathematics, University of Salerno, Via Ponte don Melillo, Fisciano, Salerno, Italy

### An efficient computational method for local fractional

The present article deals with the local fractional linear transport eq() in fractal porous media. LFLTE play a key role in diﬀerent scientiﬁc problems such as aeronomy, superconductor, semiconductors, turbulence, gas mixture, plasma and biol-ogy. A numerical scheme namely q-local fractional homotopy analysis transform method

### FRACTAL HEAT CONDUCTION PROBLEM SOLVED BY LOCAL FRACTIONAL

Local fractional variation iteration method: solution The non-linear local fractional eq. (2a) reads as a sum of linear L a and non-linear N a local fractional operators, L a T + N a T = 0 which allows the following correction functional to be constructed. We can construct a correction functional as : T t Tt I LTs NT s nnt 1 t nn 0