An efficient computational technique for local fractional heat conduction equations in fractal media

Abstract

The key aim of this article is to present an efficient numerical algorithm based on local fractional homotopy perturbation Sumudu transform technique for solving local fractional heat-conduction equations in fractal media. The proposed technique is an effective combination of local fractional homotopy perturbation method (LFHPM) and local fractional Sumudu transform algorithm. The results obtained by using the suggested scheme show that the approach is straightforward to apply and very accurate.

On the local fractional wave equation in fractal strings

“…The local fractional derivative is discussed as where …”

“…[1][2][3][4] Many researchers worked to model wave equations from the well-known wave equations by substituting the standard derivatives by the arbitrary order derivative. 5,6 Nowadays, the local fractional calculus 7 is tried to report the nondifferentiable problems, for example, heat conduction problem involving local derivative of fractional order, 7,8 local fractional Tricomi equation, 9 fractal vehicular traffic flow, 10 Laplace equation containing local fractional operator, 11 nonlinear gas dynamics equation, and coupled KdV equation pertaining to local operator of noninteger order, 12 the wave equation involving noninteger order derivative introduced by Yang, 13 the system of partial differential equations with local operator of noninteger order, 14 heat conduction equations with local fractional calculus, 15 nonlinear Riccati differential equations involving local fractional operator, 16 local fractional telegraph equations occurring in electrical transmission line, 17 local fractional LWR equation, 18 local fractional modeling in growths of populations, 19 local fractional model is used in kidney images enhancement, 20 Fitzhugh-Nagumo equations with local fractional derivative, 21 mathematical model of shallow water waves with the aid of local fractional KdV equation, 22 Boussinesq equation containing local fractional operator, 23 local fractional KdV equation, and its exact traveling wave solution, 24 etc.…”

“…The local fractional derivative is discussed as [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]…”

A new technique for solving the 1-D burgers equation

“…The non-linear diffusion equation, structured by Burgers [1], was proposed for describing the turbulence [2], acoustic waves [3], thermo-viscous fluids [4], and water wave [5]. There are many computational methods for handling the problem, such as the variable separation method [6], explicit finite difference method [7], Cole-Hopf procedure transform [8], least-squares quadratic B-spline finite element method [9], shock-capturing finite difference method [10], tanh-coth method [11], Riccati equation rational expansion method [12], and others [13][14][15][16][17][18][19][20].…”

Positive solution of nonlinear fractional differential equations with Caputo‐like counterpart hyper‐Bessel operators

“…[18][19][20][21][22][23][24][25] Some efficient analytical approaches and computational techniques were studied in previous studies. [26][27][28] Compared with methods of numerical algorithm, the development of analytical methods is always delayed because of the less of analyticity of solutions in many cases. 29,30 Gronwall-type inequality is a useful analytic method that plays a very important role 9,31-35 in the qualitative theory of fractional differential equations.…”