A fractional diffusion equation model for cancer tumor

Iyiola, Olaniyi S.; Zaman, F. D.

doi:10.1063/1.4898331

Cited by 88 publications

(61 citation statements)

References 12 publications

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“…Therefore, many analytical methods have been put to use successfully to obtain solutions of classical gas dynamics equations such as Adomian Decomposition Method (ADM) [15], Variational Iteration Method (VIM) [13], Homotopy Perturbation Method (HPM) [1], [15] and the timefractional type was considered using differential transform method (DTM) in [3]. Recently, a modified HAM called q-Homotopy Analysis Method was introduced in [4], see also [6], [8], [9], [10]. It was proven that the presence of fraction factor in this method enables a fast convergence compared to the usual HAM.…”

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confidence: 99%

On the Solutions of Non-Linear Time-Fractional Gas Dynamic Equations: An Analytical Approach

Iyiola¹

2015

Int. J. of Pure and Appl. Math.

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We consider non-linear homogeneous and non-homogeneous gas dynamic equations of time-fractional type in this paper. The approximate solutions of these equations are calculated in the form of series obtained by q-Homotopy Analysis Method (q-HAM). Exact solution is obtained for timefractional homogeneous case while for the case of time-fractional non-homogeneous, exact solution is possible for special case. This is due to the ability to control the auxiliary parameter h and the fraction factor present in this method. The presence of fraction-factor in this method gives it an edge over other existing analytical methods for non-linear differential equations. Comparisons are made with several other analytical methods.

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confidence: 99%

On the Solutions of Non-Linear Time-Fractional Gas Dynamic Equations: An Analytical Approach

Iyiola¹

2015

Int. J. of Pure and Appl. Math.

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“…describes the so called Levy flights that correspond to the continuous time random walk model, where both the mean waiting time and the jump length variance of the diffusing Particles are divergent (Luchko, 2016). Time fractional diffusion equations in the Caputo sense with initial conditions are used to model cancer tumor (Iyiola and Zaman, 2014). Nonlinear diffusion equations play a great role to describe the density dynamics in a material undergoing diffusion in a dynamic system which includes different branches of science and technology.…”

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confidence: 99%

Analytic solutions of time fractional diffusion equations by fractional reduced differential transform method (FRDTM)

Kenea¹

2018

Afr. J. Math. Comput. Sci. Res.

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This paper examines a general recurrence relation by the use of fractional reduced differential transform and then a scheme (methodology) on how to find closed solutions of one dimensional time fractional diffusion equations with initial conditions in the form of infinite fractional power series and in terms of Mittag-Leffler function in one parameter as well as their exact solutions by the use of fractional reduced differential transform method. The new general recurrence relation and the methodology of the fractional reduced differential transform method were successfully developed. The obtained new general recurrence relation helps us to solve time-fractional diffusion equations with initial conditions and various external forces by using fractional reduced differential transform method. To see its effectiveness and applicability, five test examples were presented. The results show that the general recurrence relation works successfully in solving time-fractional diffusion equations in a direct way without using linearization, transformations, perturbation, discretization or restrictive assumptions by using fractional reduced differential transform method.

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Section: Introductionmentioning

confidence: 99%

Vectorial Iterative Fractional Laplace Transform Method for the Analytic Solutions of Fractional Cauchy-Riemann Systems Partial Differential Equations

Kenea

2020

ARJOM

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The present study aims to obtain infinite fractional power series solution vectors of fractional Cauchy-Riemann systems equations with initial conditions by the use of vectorial iterative fractional Laplace transform method (VIFLTM). The basic idea of the VIFLTM was developed successfully and applied to four test examples to see its effectiveness and applicability. The infinite fractional power series form solutions were successfully obtained analytically. Thus, the results show that the VIFLTM works successfully in solving fractional Cauchy-Riemann system equations with initial conditions, and hence it can be extended to other fractional differential equations.

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A fractional diffusion equation model for cancer tumor

Cited by 88 publications

References 12 publications

On the Solutions of Non-Linear Time-Fractional Gas Dynamic Equations: An Analytical Approach

On the Solutions of Non-Linear Time-Fractional Gas Dynamic Equations: An Analytical Approach

Analytic solutions of time fractional diffusion equations by fractional reduced differential transform method (FRDTM)

Vectorial Iterative Fractional Laplace Transform Method for the Analytic Solutions of Fractional Cauchy-Riemann Systems Partial Differential Equations

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