Advances in the Natural transform

Belgacem, Fethi Bin Muhammad; Silambarasan, Rathinavel

doi:10.1063/1.4765477

Cited by 90 publications

(79 citation statements)

References 1 publication

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“…43 The NDM is a graceful mixture of the ADM and NTM. 44 Recently, many researchers employed FNDM to solve various problems that exist in science and technology. 45,46 To present the fundamental idea proposed algorithm, we consider a system of fractional-order nonlinear partial differential equation of the form…”

Section: Case (I): Fractional Natural Decomposition Methodsmentioning

confidence: 99%

Two novel computational techniques for fractional Gardner and Cahn‐Hilliard equations

Prakasha

Veeresha

Baskonus

2019

Comp and Math Methods

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The numerical solutions for nonlinear fractional Gardner and Cahn-Hilliard equations arising in fluids flow are obtained with the aid of two novel techniques, namely, fractional natural decomposition method (FNDM) and q-homotopy analysis transform method (q-HATM). Both featured techniques are different from each other since FNDM is algorithmic by the aid of Adomian polynomial and q-HATM is defined by the help of homotopy polynomial. The numerical simulations have been conducted to verify that the proposed schemes are reliable and accurate. The outcomes are revealed through the plots and tables. The comparison of solution obtained by proposed schemes with the available solutions exhibits that both the featured schemes are methodical, efficient, and very exact in solving the nonlinear complex phenomena. KEYWORDS fractional Cahn-Hilliard equation, fractional Gardner equation, fractional natural decomposition method, q-homotopy analysis transform methodwhere is real constant. Here, v (x, t) is the wave function with scaling variables space (x) and time (t), the terms vv x and v 2 v x are symbolize by the nonlinear wave steepening, and v xxx denotes the dispersive wave effects.

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Section: Case (I): Fractional Natural Decomposition Methodsmentioning

confidence: 99%

Two novel computational techniques for fractional Gardner and Cahn‐Hilliard equations

Prakasha

Veeresha

Baskonus

2019

Comp and Math Methods

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“…The NDM is an elegant amalgamation of the Adomian decomposition method (ADM) and the natural transform method (NTM) . The proposed algorithm provides solution in terms infinite series, and the obtained series rapidly converge to a closed form exact solution; for instance, Belgacem and Silambarasan provide a proof for two fundamental results of fractional natural transform by employing duality of Natural and Laplace transform. Further, by applying the duality of Sumudu and N‐transform, Rawashdeh draws the proof for three important results.…”

Section: Introductionmentioning

confidence: 99%

Numerical solution for (2 + 1)‐dimensional time‐fractional coupled Burger equations using fractional natural decomposition method

Prakasha

Veeresha

Rawashdeh

2019

Math Methods in App Sciences

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The aim of the present work is to find the numerical solutions for time‐fractional coupled Burgers equations using a new novel technique, called fractional natural decomposition method (FNDM). Two examples are considered in order to illustrate and validate the efficiency of the proposed algorithm. The numerical simulation has been conducted to ensure the exactness of the present method, and the obtained solutions are offered graphically to reveal the applicability and reliability of the FNDM. The outcomes of the study reveal that the FNDM is computationally very effective and accurate to study the (2 + 1)‐dimensional coupled Burger equations of arbitrary order.

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“…Later, Belgacem and Silambarasan defined inverse of natural transform and studied some additional fundamental properties of its [19]. Recently, N-transform is used to find the solution of differential and integral equations [21,22,23,24,25,26,27,28].…”

Section: The Natural Transformmentioning

confidence: 99%

The approximate solutions of fractional gas dynamics equations by means of fractional natural decomposition method

Ibis¹

2017

ntmsci

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Abstract:In this work, a new practical method, which is named by the Fractional Natural Decomposition Method (FNDM), is proposed to obtain the approximate analytical solutions of fractional gas dynamics equations. The FNDM is a mixture of the Natural Transform Method and the Adomian Decomposition Method. In this method, the fractional derivatives are considered as Caputo sense and the nonlinear terms are determined by virtue of Adomian polynomials. Some test examples are given to demonstrate the efficiency and accuracy of the FNDM.

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Advances in the Natural transform

Cited by 90 publications

References 1 publication

Two novel computational techniques for fractional Gardner and Cahn‐Hilliard equations

Two novel computational techniques for fractional Gardner and Cahn‐Hilliard equations

Numerical solution for (2 + 1)‐dimensional time‐fractional coupled Burger equations using fractional natural decomposition method

The approximate solutions of fractional gas dynamics equations by means of fractional natural decomposition method

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