Exact Analytical Solutions of Nonlinear Fractional Liouville Equation by Extended Complex Method

Rehman, Mehvish Fazal Ur; Gu, Yongyi; Yuan, Wenjun

doi:10.1155/2020/8815363

Cited by 3 publications

(1 citation statement)

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“…In the present work, our main purpose is to calculate the generalized fifth-order KdV equation by the extended complex method based on the concept of Yuan et al [40][41][42][43][44][45][46]. It is a remarkable approach to attain exact analytical solutions.…”

Section: Introductionmentioning

confidence: 99%

Exact Analytical Solutions of Generalized Fifth-Order KdV Equation by the Extended Complex Method

Rehman

Yuan

2021

Journal of Function Spaces

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The recently introduced technique, namely, the extended complex method, is used to explore exact solutions for the generalized fifth-order KdV equation. Appropriately, the rational, periodic, and elliptic function solutions are obtained by this technique. The 3D graphs explain the different physical phenomena to the exact solutions of this equation. This idea specifies that the extended complex method can acquire exact solutions of several differential equations in engineering. These results reveal that the extended complex method can be directly and easily used to solve further higher-order nonlinear partial differential equations (NLPDEs). All computer simulations are constructed by maple packages.

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Section: Introductionmentioning

confidence: 99%

Exact Analytical Solutions of Generalized Fifth-Order KdV Equation by the Extended Complex Method

Rehman

Yuan

2021

Journal of Function Spaces

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Existence, uniqueness and synchronization of a fractional tumor growth model in discrete time with numerical results

Alzabut,

Dhineshbabu,

Selvam

et al. 2023

Results in Physics

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The Dynamics of a Fractional-Order Mathematical Model of Cancer Tumor Disease

et al. 2022

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This article explores the application of the reduced differential transform method (RDTM) for the computational solutions of two fractional-order cancer tumor models in the Caputo sense: the model based on cancer chemotherapeutic effects which explain the relation between chemotherapeutic drugs, tumor cells, normal cells, and immune cells using a fractional partial differential equations, and the model that describes the different cases of killing rate K of cancer cells (the killing percentage of cancer cells K (I) is dependent on the number of cells, (II) is a function of time only, and (III) is a function of space only). The solutions are presented using Mathematica software as a convergent power series with elegantly computed terms using the suggested technique. The proposed method gives new series form results for various values of gamma. To clarify the complexity of the models, we plot the two- and three-dimensional and contour graphics of the obtained solutions at varied values of fractional-order gamma and the selected system parameters. The solutions are analyzed with fractional and reduced differential transform methods to obtain an idea of invariance regarding the computed solution of the designed mathematical model. The obtained results demonstrate the efficiency and preciseness of the proposed method to achieve a better understanding of chemotherapy effects. It is observed that chemotherapy drugs boost immunity against the specific cancer by decreasing the number of tumor cells, and the killing rate K of cancerous cells depend on the cells concentration.

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Exact Analytical Solutions of Nonlinear Fractional Liouville Equation by Extended Complex Method

Cited by 3 publications

References 38 publications

Exact Analytical Solutions of Generalized Fifth-Order KdV Equation by the Extended Complex Method

Exact Analytical Solutions of Generalized Fifth-Order KdV Equation by the Extended Complex Method

Existence, uniqueness and synchronization of a fractional tumor growth model in discrete time with numerical results

The Dynamics of a Fractional-Order Mathematical Model of Cancer Tumor Disease

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