Homotopy Analysis Method for Solving Foam Drainage Equation with Space‐ and Time‐Fractional Derivatives

Fadravi, Hadi Hosseini; Nik, Hassan Saberi; Buzhabadi, R.

doi:10.1155/2011/237045

Cited by 9 publications

(3 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Numerous numerical methods, such as the Adomian decomposition method (Dahmani et al. , 2008), the Homotopy analysis method (Hosseini Fadravi et al. , 2011), the variational iteration method (Dahmani and Anber, 2010), the residual power series method (Alquran, 2014), the Improved ( G ′/ G )-expansion method (Akgul et al.…”

Section: Introductionmentioning

confidence: 99%

Fractional-order view analysis of Fisher’s and foam drainage equations within Aboodh transform

Alshehry,

Yasmin,

Shah

et al. 2024

View full text Add to dashboard Cite

PurposeThe purpose of this study is to solve two unique but difficult partial differential equations: the foam drainage equation and the nonlinear time-fractional fisher’s equation. Through our methods, we aim to provide accurate solutions and gain a deeper understanding of the intricate behaviors exhibited by these systems.Design/methodology/approachIn this study, we use a dual technique that combines the Aboodh residual power series method and the Aboodh transform iteration method, both of which are combined with the Caputo operator.FindingsWe develop exact and efficient solutions by merging these unique methodologies. Our results, presented through illustrative figures and data, demonstrate the efficacy and versatility of the Aboodh methods in tackling such complex mathematical models.Originality/valueOwing to their fractional derivatives and nonlinear behavior, these equations are crucial in modeling complex processes and confront analytical complications in various scientific and engineering contexts.

show abstract

Section: Introductionmentioning

confidence: 99%

Fractional-order view analysis of Fisher’s and foam drainage equations within Aboodh transform

Alshehry,

Yasmin,

Shah

et al. 2024

View full text Add to dashboard Cite

show abstract

“…Liao reiterated the method by inserting an auxiliary parameter h, beside another auxiliary function in his problem formulation. This parameter h can be employed in controlling the convergence of solution series obtained as the power series in p. The HAM has been implemented on a wide class of boundary and initial value problems [1][2][3][10][11][12]19,27,28,[45][46][47][48][49][50][51]58,60]. The further search of expanding the convergence region led to a modification of HAM called q-HAM, proposed by El-Tawil and Huseen [17].…”

Section: Introductionmentioning

confidence: 99%

The Delta-Homotopy Perturbation Method

Huseen

2024

Preprint

View full text Add to dashboard Cite

Homotopy perturbation and analysis methods have been widely used to obtain both approximate and exact so- lutions to nonlinear problems. In general, these two methods are based on the Taylor series with respect to an embedding parameter. Many researchers have compared the two methods and raised more concerns on the homo- topy perturbation method (HPM) because the homotopy analysis method (HAM) contains a convergence-control parameter ~: For this reason, in this article, a more general form of HPM is introduced as the -homotopy per- turbation method (-HPM), which contains a control parameter : The introduction of parameter in this new modication gives a better way to adjust and control the convergence region and the rate of the series solution. We conrm through the given examples in this study that the HPM is a special case of the -HPM. The error and convergence analysis of this proposed method are also presented

show abstract

“…( 1) and its application in Ref. [24]. When α = r = 1, p = 1/2, q = −2, the generalized time fractional foam drainage equation (1) reduces to the foam drainage equation of the form…”

Section: Introductionmentioning

confidence: 99%

Lie Symmetry Analysis and Conservation Laws of a Generalized Time Fractional Foam Drainage Equation

Wang

Tian

Zhao

et al. 2016

Commun. Theor. Phys.

View full text Add to dashboard Cite

In this paper, a generalized time fractional nonlinear foam drainage equation is investigated by means of the Lie group analysis method. Based on the Riemann-Liouville derivative, the Lie point symmetries and symmetry reductions of the equation are derived, respectively. Furthermore, conservation laws with two kinds of independent variables of the equation are performed by making use of the nonlinear self-adjointness method.

show abstract

Homotopy Analysis Method for Solving Foam Drainage Equation with Space‐ and Time‐Fractional Derivatives

Cited by 9 publications

References 28 publications

Fractional-order view analysis of Fisher’s and foam drainage equations within Aboodh transform

Fractional-order view analysis of Fisher’s and foam drainage equations within Aboodh transform

The Delta-Homotopy Perturbation Method

Lie Symmetry Analysis and Conservation Laws of a Generalized Time Fractional Foam Drainage Equation

Contact Info

Product

Resources

About