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Journal ArticleDOI

Natural homotopy perturbation method for solving nonlinear fractional gas dynamics equations

01 Feb 2021-International Journal of Nonlinear Analysis and Applications (Semnan University)-Vol. 12, Iss: 1, pp 812-820
TL;DR: In this article, the authors investigate solutions of nonlinear fractional differential equations by using Natural homotopy perturbation method (NHPM) and Natural transform (NT) coupled by the Natural transform and HPM.
Abstract: In this paper, we investigate solutions of nonlinear fractional differential equations by using Natural homotopy perturbation method (NHPM). This method is coupled by the Natural transform (NT) and homotopy perturbation method (HPM). The method in general is easy to implement and yields good results. Illustrative examples are included to demonstrate the validity and applicability of the presented method.
Citations
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Journal ArticleDOI
TL;DR: In this article, the Sumudu homotopy perturbation method (SHPM) is applied to solve fractional order nonlinear differential equations in this paper, the results obtained by FSHPM are in acceptable concurrence with the specific arrangement of the problem.
Abstract: The Sumudu homotopy perturbation method (SHPM) is applied to solve fractional order nonlinear differential equations in this paper.The current technique incorporates two notable strategies in particular Sumudu transform (ST) and homotopy perturbation method (HPM). The proposed method’s hybrid property decreases the number of the quantity of computations and materials needed. In this method, illustration examples evaluate the accuracy and applicability of the mentioned procedure. The outcomes got by FSHPM are in acceptable concurrence with the specific arrangement of the problem.

6 citations

Journal ArticleDOI
TL;DR: In this paper , the Sumudu transform and the homotopy perturbation technique are combined to solve time fractional linear and nonlinear partial differential equations, and the fractional derivative is defined.
Abstract: This paper shows how to use the fractional Sumudu homotopy perturbation technique (SHP) with the Caputo fractional operator (CF) to solve time fractional linear and nonlinear partial differential equations. The Sumudu transform (ST) and the homotopy perturbation technique (HP) are combined in this approach. In the Caputo definition, the fractional derivative is defined. In general, the method is straightforward to execute and yields good results. There are some examples offered to demonstrate the technique's validity and use.

5 citations

Journal ArticleDOI
TL;DR: In this article , Hussein-Jassim (HJ) method is proposed for solving nonlinear fractional ODEs. But the proposed method is based on a power series of fractional order.
Abstract: Recently, researchers have been interested in studying fractional differential equations and their solutions due to the wide range of their applications in many scientific fields. In this paper, a new approach called the Hussein–Jassim (HJ) method is presented for solving nonlinear fractional ordinary differential equations. The new method is based on a power series of fractional order. The proposed approach is employed to obtain an approximate solution for the fractional differential equations. The results of this study show that the solutions obtained from solving the fractional differential equations are highly consistent with those obtained by exact solutions.

3 citations

References
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01 Jan 2012

433 citations


"Natural homotopy perturbation metho..." refers background in this paper

  • ...Introduction In recent years, many researchers have paid attention to study the behavior of physical problems by using various analytical and numerical techniques which are not described by the common observations, such as the FVIM [1, 2, 3, 4, 5], FDTM [6, 7], FSEM [8, 9], FSTM [10], FLTM [11, 12], FHPM [13], FLDM [14, 15], FFSM [16], FLVIM [17, 18, 19, 20] and another methods [21, 22, 23, 24, 25, 26, 27, 28, 29]....

    [...]

  • ...In recent years, many researchers have paid attention to study the behavior of physical problems by using various analytical and numerical techniques which are not described by the common observations, such as the FVIM [1, 2, 3, 4, 5], FDTM [6, 7], FSEM [8, 9], FSTM [10], FLTM [11, 12], FHPM [13], FLDM [14, 15], FFSM [16], FLVIM [17, 18, 19, 20] and another methods [21, 22, 23, 24, 25, 26, 27, 28, 29]....

    [...]

01 Jan 2011

228 citations


"Natural homotopy perturbation metho..." refers background in this paper

  • ...Introduction In recent years, many researchers have paid attention to study the behavior of physical problems by using various analytical and numerical techniques which are not described by the common observations, such as the FVIM [1, 2, 3, 4, 5], FDTM [6, 7], FSEM [8, 9], FSTM [10], FLTM [11, 12], FHPM [13], FLDM [14, 15], FFSM [16], FLVIM [17, 18, 19, 20] and another methods [21, 22, 23, 24, 25, 26, 27, 28, 29]....

    [...]

  • ...In recent years, many researchers have paid attention to study the behavior of physical problems by using various analytical and numerical techniques which are not described by the common observations, such as the FVIM [1, 2, 3, 4, 5], FDTM [6, 7], FSEM [8, 9], FSTM [10], FLTM [11, 12], FHPM [13], FLDM [14, 15], FFSM [16], FLVIM [17, 18, 19, 20] and another methods [21, 22, 23, 24, 25, 26, 27, 28, 29]....

    [...]

Journal ArticleDOI
TL;DR: It can be observed that the auxiliary parameter ℏ, which controls the convergence of the HATM approximate series solutions, also can be used in predicting and calculating multiple solutions.

136 citations

Journal ArticleDOI
05 Oct 2015-Entropy
TL;DR: The obtained result shows the non-differentiable behavior of heat conduction of the fractal temperature field in homogeneous media in the sense of the local fractional differential operator.
Abstract: 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.

102 citations


"Natural homotopy perturbation metho..." refers background in this paper

  • ...Introduction In recent years, many researchers have paid attention to study the behavior of physical problems by using various analytical and numerical techniques which are not described by the common observations, such as the FVIM [1, 2, 3, 4, 5], FDTM [6, 7], FSEM [8, 9], FSTM [10], FLTM [11, 12], FHPM [13], FLDM [14, 15], FFSM [16], FLVIM [17, 18, 19, 20] and another methods [21, 22, 23, 24, 25, 26, 27, 28, 29]....

    [...]

  • ...In recent years, many researchers have paid attention to study the behavior of physical problems by using various analytical and numerical techniques which are not described by the common observations, such as the FVIM [1, 2, 3, 4, 5], FDTM [6, 7], FSEM [8, 9], FSTM [10], FLTM [11, 12], FHPM [13], FLDM [14, 15], FFSM [16], FLVIM [17, 18, 19, 20] and another methods [21, 22, 23, 24, 25, 26, 27, 28, 29]....

    [...]

Journal ArticleDOI
TL;DR: In this paper, a coupling method of Sumudu transform and local fractional calculus is proposed to find the non-differentiable analytical solutions for initial value problems with LFT derivatives.
Abstract: Local fractional derivatives were investigated intensively during the last few years. The coupling method of Sumudu transform and local fractional calculus (called as the local fractional Sumudu transform) was suggested in this paper. The presented method is applied to find the nondifferentiable analytical solutions for initial value problems with local fractional derivative. The obtained results are given to show the advantages.

84 citations


"Natural homotopy perturbation metho..." refers background in this paper

  • ...Introduction In recent years, many researchers have paid attention to study the behavior of physical problems by using various analytical and numerical techniques which are not described by the common observations, such as the FVIM [1, 2, 3, 4, 5], FDTM [6, 7], FSEM [8, 9], FSTM [10], FLTM [11, 12], FHPM [13], FLDM [14, 15], FFSM [16], FLVIM [17, 18, 19, 20] and another methods [21, 22, 23, 24, 25, 26, 27, 28, 29]....

    [...]

  • ...In recent years, many researchers have paid attention to study the behavior of physical problems by using various analytical and numerical techniques which are not described by the common observations, such as the FVIM [1, 2, 3, 4, 5], FDTM [6, 7], FSEM [8, 9], FSTM [10], FLTM [11, 12], FHPM [13], FLDM [14, 15], FFSM [16], FLVIM [17, 18, 19, 20] and another methods [21, 22, 23, 24, 25, 26, 27, 28, 29]....

    [...]