A Reliable Algorithm for a Local Fractional Tricomi Equation Arising in Fractal Transonic Flow

Singh, Jagdev; Kumar, Devendra; Nieto, Juan J.

doi:10.3390/e18060206

Cited by 82 publications

(44 citation statements)

References 27 publications

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“…More recently, local fractional calculus (LFC) [24,26] was applied to discuss the non-differentiable problems, for instance, the local fractional heat-conduction [31][32][33], Tricomi [16], diffusion [9], damped and dissipative wave [18], Laplace [23] and Fokker-Planck equations [12], and electric circuit [27], etc.…”

Section: Introductionmentioning

confidence: 99%

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

Duan¹,

Singh²,

Kumar³

et al. 2017

J. Nonlinear Sci. Appl.

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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.

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Section: Introductionmentioning

confidence: 99%

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

Duan¹,

Singh²,

Kumar³

et al. 2017

J. Nonlinear Sci. Appl.

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“…The following section is dedicated to the introduction of the main steps of the exploited method (LHPSTM) [33]. To illustrate this, we consider the next local fractional differential problem:…”

Section: Local Fractional Sumudu Transform Coupled With Homotopy Pertmentioning

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 model of fractional differential equations have been showed beyond doubt to be an excellent tool to reveal the hidden aspect in various field of science and engineering associated with non-locality [1,3,4,9,32]. These successes lead up with proposed techniques to system of time-fractional differential equations occurring in HIV infection of CD4 + T lymphocyte cells.…”

Section: Introductionmentioning

confidence: 99%

Analytic study for a fractional model of HIV infection of C D 4 + T lymphocyte cells

Bulut¹,

Kumar²,

Singh³

et al. 2018

Math. Nat. Sci.

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In this article, we implemented homotopy transform methods, namely, homotopy analysis transform method and homotopy perturbation Sumudu transform method to examine the fractional model for HIV infection of CD4 + T lymphocyte cells. Proliferation of CD4 + T lymphocyte cells is driven by a combination of the homeostatic response to cells depletion (CD4 + T cells counts) and viral load (HIV levels). The attraction of both the methods is that an approach of HPSTM is used and on other hand by HATM a large admissible convergence range of series solution is described for standard as well as fractional order nonlinear problems.

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A Reliable Algorithm for a Local Fractional Tricomi Equation Arising in Fractal Transonic Flow

Cited by 82 publications

References 27 publications

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

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

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

Analytic study for a fractional model of HIV infection of C D 4 + T lymphocyte cells

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