Solution of Moving Boundary Space-Time Fractional Burger’s Equation

Abdel-Salam, Emad A.-B.; Yousif, Eltayeb A.; Arko, Yagoub A. S.; Gumma, Elzain A.E.

doi:10.1155/2014/218092

Cited by 16 publications

(9 citation statements)

References 51 publications

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“…The space‐time fractional Burger's equation, which is a transformed generalization of the Burger's equation, is defined as follows :

D_{t}^{α} u = σ D_{x}^{2 α} u + 2 δu D_{x}^{α} u, 0 < α \leq 1,

where u = u ( x , t ), σ , δ are arbitrary constants and α is the fractional order derivative. Burger's equation is a classical nonlinear differential equation, which was firstly introduced by Burger in 1948.…”

Section: The Space‐time Fractional Burger's Equationmentioning

confidence: 99%

On the concept of exact solution for nonlinear differential equations of fractional‐order

Güner

Bekir

2016

Math Methods in App Sciences

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In this article, the new exact travelling wave solutions of the nonlinear space-time fractional Burger's, the nonlinear spacetime fractional Telegraph and the nonlinear space-time fractional Fisher equations have been found. Based on a nonlinear fractional complex transformation, certain fractional partial differential equations can be turned into ordinary differential equations of integer order in the sense of the Jumarie's modified Riemann-Liouville derivative. The-expansion method is effective for constructing solutions to the nonlinear fractional equations, and it appears to be easier and more convenient by means of a symbolic computation system.

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“…The space‐time fractional Burger's equation, which is a transformed generalization of the Burger's equation, is defined as follows :

D_{t}^{α} u = σ D_{x}^{2 α} u + 2 δu D_{x}^{α} u, 0 < α \leq 1,

Section: The Space‐time Fractional Burger's Equationmentioning

confidence: 99%

On the concept of exact solution for nonlinear differential equations of fractional‐order

Güner

Bekir

2016

Math Methods in App Sciences

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“…Within the context, fractional calculus deals with the situations wherein the order of the operator can be arbitrarily complex-valued [25,26]. In this stream, the fractional dimensional (FD) space remains a key tool to analyze problems in physics and engineering [27][28][29]. While simple geometries and smooth surfaces can be represented using canonical shapes, most of the practical objects embody irregularity and complexities in shape, and thus, are modeled using the FD space [30].…”

Section: Introductionmentioning

confidence: 99%

On the Core-Shell Nanoparticle in Fractional Dimensional Space

et al. 2020

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The investigation of core-shell nanoparticles has been greatly exciting in biomedical applications, as this remains of prime importance in targeted drug delivery, sensing, etc. In the present work, the polarizability and scattering features of nanoparticles comprised of nano-sized dielectric/metallic core-shell structures were investigated in the fractional dimensional (FD) space, which essentially relates to the confinement of charged particles. For this purpose, three different kinds of metals—namely aluminum, gold and silver—were considered to form the shell, having a common silicon dioxide (SiO2) nanoparticle as the core. It is noteworthy that the use of noble metal-SiO2 mediums interface remains ideal to realize surface plasmon resonance. The core-shell nanoparticles were considered to have dimensions smaller than the operating wavelength. Under such conditions, the analyses of polarizability and the scattering and absorption cross-sections, and also, the extinction coefficients were taken up under Rayleigh scattering mechanism, emphasizing the effects of a varying FD parameter. Apart from these, the tuning of resonance peaks and the magnitude of surface plasmons due to FD space parameter were also analyzed. It was found that the increase of FD space parameter generally results in blue-shifts in the resonance peaks. Apart from this, the usage of gold and silver shells brings in fairly large shifts in the peak positions of wavelengths, which allows them to be more suitable for a biosensing purpose.

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“…During the last few years, the exact solution methods have been proposed for solving fractional di erential equations, e.g. the functional variable method [8], the rst integral method [9], the exp-function method [10], fractional Riccati expansion method [11][12], and so on [13][14]. Eqs.…”

Section: Introductionmentioning

confidence: 99%

Sub-equation method for the fractional regularized long-wave equations with conformable fractional derivatives

2016

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In this paper, we employ a sub-equation method to nd the exact solutions to the fractional (1 + 1) and (2 + 1) regularized long-wave equations which arise in several physical applications, including ion sound waves in plasma, by using a new de nition of fractional derivative called conformable fractional derivative. The presented method is more e ective, powerful, and straightforward and can be used for many other nonlinear partial fractional di erential equations.

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Solution of Moving Boundary Space-Time Fractional Burger’s Equation

Cited by 16 publications

References 51 publications

On the concept of exact solution for nonlinear differential equations of fractional‐order

On the concept of exact solution for nonlinear differential equations of fractional‐order

On the Core-Shell Nanoparticle in Fractional Dimensional Space

Sub-equation method for the fractional regularized long-wave equations with conformable fractional derivatives

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