An efficient method for solving nonlinear time-fractional wave-like equations with variable coefficients

Khalouta, Ali; Kadem, Abdelouahab

doi:10.32513/tbilisi/1578020573

Cited by 9 publications

(10 citation statements)

References 15 publications

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“…where E α (−t α ) and E α,2 (−t α ) are the Mittag-Leffler functions, defined by Eqs. which is the same result as those obtained by the NIM and NHPM [8] for the same example. The surface and behavior of the solution for this example is graphically presented in Figures 1 and 2 for different fractional orders of α.…”

Section: Then the General Term In Successive Approximation Is Given Bysupporting

confidence: 89%

A new technique for finding exact solutions of nonlinear time-fractional wave-like equations with variable coefficients

Khalouta¹

2019

edu

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In this paper, we give the exact solutions in terms of Mittag-Leffler functions for nonlinear time-fractional wave-like equations with variable coefficients by using a new technique, it is a combination of natural transform and variational iteration method called natural variational iteration method (NVIM). This technique enables us to overcome the difficulties arising in identifying the general Lagrange multiplier. The numerical results shows that this method is highly effective and is practically suitable for use in these equations. Three numerical examples are given to verify the accuracy and efficiency of the proposed technique.

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Section: Then the General Term In Successive Approximation Is Given Bysupporting

confidence: 89%

A new technique for finding exact solutions of nonlinear time-fractional wave-like equations with variable coefficients

Khalouta¹

2019

edu

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“…which is the same solution as obtained by using the FRPSM [25]. Tables 1, 2 and 3 show the comparison between the FRPSM-approximate solutions (see [25]) and the obtained results by the MRDTM. From these tables, we can see that the solution obtained by the MRDTM match well with the FRPSM and coincide with the exact solution.…”

Section: Numerical Examplesmentioning

confidence: 70%

“…which is the same solution as obtained by using the FRPSM [25]. Example 3 Consider the following one dimensional nonlinear time-fractional wave-like equation with variable coefficients…”

Section: Numerical Examplesmentioning

confidence: 86%

A new modification of the reduced differential transform method for nonlinear fractional partial differential equations

Khalouta¹,

Kadem²

2020

J. Appl. Math. Comput. Mech.

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The objective of this study is to present a new modification of the reduced differential transform method (MRDTM) to find an approximate analytical solution of a certain class of nonlinear fractional partial differential equations in particular, nonlinear time-fractional wave-like equations with variable coefficients. This method is a combination of two different methods: the Shehu transform method and the reduced differential transform method. The advantage of the MRDTM is to find the solution without discretization, linearization or restrictive assumptions. Three different examples are presented to demonstrate the applicability and effectiveness of the MRDTM. The numerical results show that the proposed modification is very effective and simple for solving nonlinear fractional partial differential equations.

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“…There are several numerical methods given for solving fractional differential equations. The most used ones are: Adomian decomposition method (ADM) [8], variational iteration method (VIM) [16], new iterative method (NIM) [13], differential transform method (DTM) [5], homotopy perturbation method (HPM) [1] and homotopy analysis method (HAM) [11].…”

Section: Introductionmentioning

confidence: 99%

Solution of the Fractional Bratu-Type Equation Via Fractional Residual Power Series Method

Khalouta

Kadem

2020

Tatra Mountains Mathematical Publications

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In this paper, we present numerical solution for the fractional Bratu-type equation via fractional residual power series method (FRPSM). The fractional derivatives are described in Caputo sense. The main advantage of the FRPSM in comparison with the existing methods is that the method solves the nonlinear problems without using linearization, discretization, perturbation or any other restriction. Three numerical examples are given and the results are numerically and graphically compared with the exact solutions. The solutions obtained by the proposed method are in complete agreement with the solutions available in the literature. The results reveal that the FRPSM is a very effective, simple and efficient technique to handle a wide range of fractional differential equations.

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An efficient method for solving nonlinear time-fractional wave-like equations with variable coefficients

Cited by 9 publications

References 15 publications

A new technique for finding exact solutions of nonlinear time-fractional wave-like equations with variable coefficients

A new technique for finding exact solutions of nonlinear time-fractional wave-like equations with variable coefficients

A new modification of the reduced differential transform method for nonlinear fractional partial differential equations

Solution of the Fractional Bratu-Type Equation Via Fractional Residual Power Series Method

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