Initial boundary value problem for fractal heat equation in the semi-infinite region by Yang-Laplace transform

Zhang, Yuzhu; Yang, Aimin; Long, Yue

doi:10.2298/tsci130901152z

Cited by 48 publications

(40 citation statements)

References 26 publications

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“…In this section, we present the basic theory of LFDO [16][17][18][19][20][21][22][23][24][25][26][27][28][29]. The LFDO of Θ (µ) of ε order (0 < ε ≤ 1) is defined by…”

Section: The Lfdomentioning

confidence: 99%

“…The comparison between diffusion problem via local fractional time-and space-derivative operators and classical one was presented in [24]. The fractal heat conduction equation with the help of local fractional time-and space-derivative operators was discussed by using the local fractional Laplace operator [25]. For more applications in integral transforms and fluid mechanics, see [26][27][28].…”

Section: Introductionmentioning

confidence: 99%

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Local Fractional Homotopy Perturbation Method for Solving Non-Homogeneous Heat Conduction Equations in Fractal Domains

Cattani

Yang

2015

Entropy

103

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In this article, the local fractional Homotopy perturbation method is utilized to solve the non-homogeneous heat conduction equations. The operator is considered in the sense of the local fractional differential operator. Comparative results between non-homogeneous and homogeneous heat conduction equations are presented. The obtained result shows the non-differentiable behavior of heat conduction of the fractal temperature field in homogeneous media.

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“…In this section, we present the basic theory of LFDO [16][17][18][19][20][21][22][23][24][25][26][27][28][29]. The LFDO of Θ (µ) of ε order (0 < ε ≤ 1) is defined by…”

Section: The Lfdomentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Local Fractional Homotopy Perturbation Method for Solving Non-Homogeneous Heat Conduction Equations in Fractal Domains

Cattani

Yang

2015

Entropy

103

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“…Therefore, numerous analytical and numerical methods were successfully utilized to treat this sort of problems. Among the aforementioned methods, we can refer to fractional Homotopy Perturbation [14], fractional Adomian decomposition [15], Yang-Laplace transform [16], Variational Iteration and function decomposition in local fractional sense [15,17].…”

Section: Introductionmentioning

confidence: 99%

Implementation and Convergence Analysis of Homotopy Perturbation Coupled With Sumudu Transform to Construct Solutions of Local-Fractional PDEs

et al. 2018

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Abstract:In the present paper, the explicit solutions of some local fractional partial differential equations are constructed through the integration of local fractional Sumudu transform and homotopy perturbation such as local fractional dissipative and damped wave equations. The convergence aspect of this technique is also discussed and presented. The obtained results prove that the employed method is very simple and effective for treating analytically various kinds of problems comprising local fractional derivatives.

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“…The heat conduction equation was discussed by the help of local fractional derivative (LFD) [26]. Some numerical methods are applied to many non-differentiable problems in Cantor sets by using LFD [21][22][23][24][25][26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Analytical Approximate Solutions of (n + 1)-Dimensional Fractal Heat-Like and Wave-Like Equations

Acan

Băleanu

Qurashi

et al. 2017

Entropy

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Abstract:In this paper, we propose a new type (n + 1)-dimensional reduced differential transform method (RDTM) based on a local fractional derivative (LFD) to solve (n + 1)-dimensional local fractional partial differential equations (PDEs) in Cantor sets. The presented method is named the (n + 1)-dimensional local fractional reduced differential transform method (LFRDTM). First the theories, their proofs and also some basic properties of this procedure are given. To understand the introduced method clearly, we apply it on the (n + 1)-dimensional fractal heat-like equations (HLEs) and wave-like equations (WLEs). The applications show that this new technique is efficient, simply applicable and has powerful effects in (n + 1)-dimensional local fractional problems.

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Initial boundary value problem for fractal heat equation in the semi-infinite region by Yang-Laplace transform

Abstract: Analytical solution of transient heat conduction through a semi-infinite fractal medium is developed. The solution focuses on application of a local fractional derivative operator to model the heat transfer process and a solution through theYang-Laplace transform.

Cited by 48 publications

References 26 publications

Local Fractional Homotopy Perturbation Method for Solving Non-Homogeneous Heat Conduction Equations in Fractal Domains

Local Fractional Homotopy Perturbation Method for Solving Non-Homogeneous Heat Conduction Equations in Fractal Domains

Implementation and Convergence Analysis of Homotopy Perturbation Coupled With Sumudu Transform to Construct Solutions of Local-Fractional PDEs

Analytical Approximate Solutions of (n + 1)-Dimensional Fractal Heat-Like and Wave-Like Equations

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