Analytical Solution of Fractional Burgers-Huxley Equations via Residual Power Series Method

Freihet, Asad; Zuriqat, M.

doi:10.1134/s1995080219020082

Cited by 15 publications

(6 citation statements)

References 17 publications

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“…Table 1 displays our acquired numerical results as well as the exact solutions of Example 1 for the integer‐order, where all numerical solutions in the classical situation of integer order are identical, and the comparison result agrees well with the RPS approach [52]. The test example demonstrates the suggested method's efficiency, flexibility, and correctness.…”

Section: Numerical Outcomes and Discussionmentioning

confidence: 58%

“…Lie symmetry analysis and the power series expansion method are used to illustrate the time fractional generalized Burgers–Huxley equation in [51]. The authors of [52] used the residual power series (RPS) technique to approximate the time fractional Burgers–Huxley equation. In [53], a novel approach for obtaining approximate results for the time fractional Burgers–Huxley equation is presented that combines the line and group preserving methods.…”

Section: Introductionmentioning

confidence: 99%

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Natural transform decomposition method for the numerical treatment of the time fractional Burgers–Huxley equation

Kanth

Aruna

Raghavendar

2022

Numerical Methods Partial

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In this article, we studied the time-fractional Burgers-Huxley equation using the natural transform decomposition method. The fractional operator is treated in the Caputo, Caputo-Fabrizio, and Atangana-Baleanu senses. We employed the natural transform with the Adomian decomposition process on time-fractional Burgers-Huxley equation to obtain the solution. To establish the uniqueness and convergence of the accomplished solution, the Banach's fixed point theorem is used. The obtained findings are visually shown in two-and three-dimensional graphs for various fractional orders. To illustrate the efficacy of the method under discussion, numerical simulations are provided. The proposed solution captures the behavior of the reported findings for various fractional orders. A comparative study was conducted to ascertain the proposed method's correctness. The findings of this study establish that the technique investigated is both efficient and accurate for solving nonlinear fractional differential equations that arise in science and technology.

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Section: Numerical Outcomes and Discussionmentioning

confidence: 58%

Section: Introductionmentioning

confidence: 99%

Natural transform decomposition method for the numerical treatment of the time fractional Burgers–Huxley equation

Kanth

Aruna

Raghavendar

2022

Numerical Methods Partial

View full text Add to dashboard Cite

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“…In recent decades, the study of fractional differential equations (FDEs) became an attractive field due to its significant and notable application in several areas of science. Consequently, it has become necessary to develop and present new methods and approaches to derive numerical and analytical solutions for this type of equation (see, e.g., [18][19][20][21][22][23][24][25][26][27][28][29][30]). This paper deals with the time-fractional mKdV-ZK equation:…”

Section: Introductionmentioning

confidence: 99%

Traveling Wave Solutions for Time-Fractional mKdV-ZK Equation of Weakly Nonlinear Ion-Acoustic Waves in Magnetized Electron–Positron Plasma

et al. 2023

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In this paper, we discuss the time-fractional mKdV–ZK equation, which is a kind of physical model, developed for plasma of hot and cool electrons and some fluid ions. Based on the properties of certain employed truncated M-fractional derivatives, we reduce the time-fractional mKdV–ZK equation to an integer-order ordinary differential equation utilizing an adequate traveling wave transformation. Further, we derive a dynamical system to present bifurcation of the equation equilibria and show existence of solitary and kink singular wave solutions for the time-fractional mKdV–ZK equation. Furthermore, we establish symmetric solitary, kink, and singular wave solutions for the governing model by using the ansatz method. Moreover, we depict desired results at different physical parameter values to provide physical interpolations for the aforementioned equation. Finally, we introduce applications of the governing model in detail.

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“…Many researchers have worked hard to find the solutions to FPDEs by using RPSM and other novel techniques that have been used for the solutions of FPDEs like: Senol et al [38] solved the timefractional nonlinear coupled Jaulent-Miodek system with energy-dependent Schrodinger Potential using RPSM in 2019, Korpinar et al [39] have analysed the solution of the fractional cancer model by RPSM, Kurt [40] has implemented RPSM to obtain the solution of fractional Bogoyavlensky-Konopelchenko equation, Xu et al [41] have implemented RPSM to obtain the solution of fractional Boussinesq equations, Freihet et al [42] have found the solution of fractional Burgers-Huxley equations in by using RPSM. Jena et al [43] have found the solution of the fractional model of the vibration equation of large membranes using RPSM.…”

Section: Introductionmentioning

confidence: 99%

The Fractional Investigation of Fornberg-Whitham Equation Using an Efficient Technique

Khan¹,

Nawaz²,

Khan³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

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In the last few decades, it has become increasingly clear that fractional calculus always plays a very significant role in various branches of applied sciences. For this reason, fractional partial differential equations (FPDEs) are of more importance to model the different physical processes in nature more accurately. Therefore, the analytical or numerical solutions to these problems are taken into serious consideration and several techniques or algorithms have been developed for their solution. In the current work, the idea of fractional calculus has been used, and fractional Fornberg Whitham equation (FFWE) is represented in its fractional view analysis. A well-known method which is residual power series method (RPSM), is then implemented to solve FFWE. The RPSM results are discussed through graphs and tables which conform to the higher accuracy of the proposed technique. The solutions at different fractional orders are obtained and shown to be convergent toward an integer-order solution. Because the RPSM procedure is simple and straightforward, it can be extended to solve other FPDEs and their systems.

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Analytical Solution of Fractional Burgers-Huxley Equations via Residual Power Series Method

Cited by 15 publications

References 17 publications

Natural transform decomposition method for the numerical treatment of the time fractional Burgers–Huxley equation

Natural transform decomposition method for the numerical treatment of the time fractional Burgers–Huxley equation

Traveling Wave Solutions for Time-Fractional mKdV-ZK Equation of Weakly Nonlinear Ion-Acoustic Waves in Magnetized Electron–Positron Plasma

The Fractional Investigation of Fornberg-Whitham Equation Using an Efficient Technique

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