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

Prakasha, D. G.; Veeresha, P.; Rawashdeh, Mahmoud S.

doi:10.1002/mma.5533

Cited by 59 publications

(31 citation statements)

References 31 publications

(56 reference statements)

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“…43 The NDM is a graceful mixture of the ADM and NTM. 45,46 To present the fundamental idea proposed algorithm, we consider a system of fractional-order nonlinear partial differential equation of the form 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%

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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%

“…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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“…There are several methods used in obtaining approximate solutions to linear and nonlinear FPDE such as the Adomian decomposition method (ADM) [28,29], the homotopyperturbation method (HPM) [30][31][32][33][34], the variational iteration method (VIM) [35], the q-homotopy analysis transform method (q-HATM) [36,37], the fractional natural decomposition method (FNDM) [38], the fractional multi-step differential transformed method (FMsDTM) [39], the new iterartive method (NIM) [40][41][42] and the homotopy analysis method (HAM) [43][44][45][46]. In a recent development, [47][48][49][50][51][52][53], a modified homotopy analysis method was established which has potential applications in a wide range of systems of differential equations.…”

Section: Introductionmentioning

confidence: 99%

Efficient analytical techniques for solving time-fractional nonlinear coupled Jaulent–Miodek system with energy-dependent Schrödinger potential

et al. 2019

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In this paper, we present analytical-approximate solution to the time-fractional nonlinear coupled Jaulent-Miodek system of equations which comes with an energy-dependent Schrödinger potential by means of a residual power series method (RSPM) and a q-homotopy analysis method (q-HAM). These methods produce convergent series solutions with easily computable components. Using a specific example, a comparison analysis is done between these methods and the exact solution. The numerical results show that present methods are competitive, powerful, reliable, and easy to implement for strongly nonlinear fractional differential equations.

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“…We can say that the proposed technique can decrease the computation of the time and work as compared with other traditional techniques while maintaining the great efficiency of the obtained results. Due to these factors, recently, many authors are employed q-HATM to analyse the complex problems occur in science and engineering [26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Solving smoking epidemic model of fractional order using a modified homotopy analysis transform method

2019

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The pivotal aim of the present work is to obtain an approximated analytical solution for the fractional smoking epidemic model with the aid of a novel technique called q-homotopy analysis transform method (q-HATM). The considered nonlinear mathematical model has been effectively employed to elucidate the evolution of smoking in a population and its impact on public health in a community. We find some new approximate solutions in a series form, which converges rapidly, and the proposed algorithm provides auxiliary parameters, which are very reliable and feasible in controlling the convergence of obtained approximate solutions. Further, we present novel simulations for all cases of results to validate the applicability and effectiveness of proposed scheme. The outcomes of the study reveal that the q-HATM is computationally very effective to analyse nonlinear fractional differential equations arises in daily life problems.

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

Cited by 59 publications

References 31 publications

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

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

Efficient analytical techniques for solving time-fractional nonlinear coupled Jaulent–Miodek system with energy-dependent Schrödinger potential

Solving smoking epidemic model of fractional order using a modified homotopy analysis transform method

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