A linearization‐based approach of homotopy analysis method for non‐linear time‐fractional parabolic PDEs
Sign Up to like & getrecommendations! Published in 2019 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.5829
Abstract: In this paper, a novel approach, namely, the linearization‐based approach of homotopy analysis method, to analytically treat non‐linear time‐fractional PDEs is proposed. The presented approach suggests a new optimized structure of the homotopy series solution… read more here.
Keywords: non linear; homotopy analysis; approach; homotopy ... See more keywords
The use of homotopy analysis method for solving generalized Sylvester matrix equation with applications
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DOI: 10.1007/s00366-020-01219-0
Abstract: In this research, we introduce and analyze homotopy analysis method (HAM) for solving approximately linear matrix equation $$ \sum \limits \limits _{i=1}^{s}A_iXB_i+C=\mathbf{0} $$ , where $$ A_i,\;B_i \;(i=1,\ldots ,s), \; C \in \mathbb {C}^{n \times… read more here.
Keywords: matrix equation; homotopy analysis; method; analysis method ... See more keywords
Solving Black–Scholes equations using fractional generalized homotopy analysis method
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DOI: 10.1007/s40314-020-01306-4
Abstract: This paper aims to solve the Black–Scholes (B–S) model for the European options pricing problem using a hybrid method called fractional generalized homotopy analysis method (FGHAM). The convergence region of the B–S model solutions are… read more here.
Keywords: black scholes; homotopy analysis; method; analysis method ... See more keywords
The Optimal Homotopy Analysis Method for solving linear optimal control problems
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DOI: 10.1016/j.apm.2017.01.024
Abstract: Abstract In this paper, an Optimal Homotopy Analysis Method (Optimal HAM) is applied to solve the linear optimal control problems (OCPs), which have a quadratic performance index. This approach contains at most two convergence-control parameters… read more here.
Keywords: control; homotopy analysis; method; analysis method ... See more keywords
On the optimal selection of the linear operator and the initial approximation in the application of the homotopy analysis method to nonlinear fractional differential equations
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DOI: 10.1016/j.apnum.2018.11.003
Abstract: Abstract In this study, an optimal homotopy analysis approach will be described to deal with nonlinear fractional differential equations. The proposed approach presents a procedure to find an optimal auxiliary linear operator and the corresponding… read more here.
Keywords: nonlinear fractional; homotopy analysis; fractional differential; differential equations ... See more keywords
θ –Parameter differential transform with homotopy analysis methods for solving nonlinear initial and boundary value problems
Sign Up to like & getrecommendations! Published in 2025 at "Arab Journal of Basic and Applied Sciences"
DOI: 10.1080/25765299.2025.2537475
Abstract: Abstract Our article deals with a new improvement of the θ-parameterized differential transformation method (θ– PDTM) by combining it with the Homotopy analysis method (HAM) for solving both the nonlinear initial and the boundary value… read more here.
Keywords: method; solving nonlinear; homotopy analysis; boundary value ... See more keywords
Inverse problem for the linear bi-flux diffusion equation using homotopy analysis method
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DOI: 10.1088/1402-4896/adbd95
Abstract: The linear bi-flux diffusion equation extends the classical diffusion process by incorporating a bimodal flux distribution. In this paper, we address an inverse problem associated with this model. Specifically, we consider the case where the… read more here.
Keywords: method; analysis method; problem; inverse problem ... See more keywords
Traveltime approximation for strongly anisotropic media using the homotopy analysis method
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DOI: 10.1093/gji/ggy524
Abstract: S U M M A R Y Traveltime approximation plays an important role in seismic data processing, for example, anisotropic parameter estimation and seismic imaging. By exploiting seismic traveltimes, it is possible to improve the… read more here.
Keywords: anisotropic media; method; equation; homotopy analysis ... See more keywords
Comparison of optimal homotopy analysis method and fractional homotopy analysis transform method for the dynamical analysis of fractional order optical solitons
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DOI: 10.1177/1687814017692946
Abstract: In this article, dynamical analysis of fractional order Schrödinger equation governing the optical wave propagation is reported in detail. The validity criteria for the application of the semi-analytic asymptotic methods are exploited. Comparison between the… read more here.
Keywords: analysis; analysis fractional; method; dynamical analysis ... See more keywords
Semianalytical solutions by homotopy analysis method for EIAV infection with stability analysis
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DOI: 10.1186/s13662-018-1808-3
Abstract: Equine Infectious Anemia Virus (EIAV) is a bovine lentivirus group that creates equine infectious anemia in horses around the globe. In this paper, we propose a basic nonlinear differential equation for EIAV infection. Moreover, we… read more here.
Keywords: analysis; eiav infection; method; homotopy analysis ... See more keywords
Homotopy-Analysis-Method-Based Solutions of Quintic Nonlinear Angular Motion for Projectiles
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DOI: 10.2514/1.a33864
Abstract: The current research literature has shown that the nonlinear aerodynamic coefficients have a significant impact on the angular motion of projectiles. However, high-order aerodynamic coefficients, s... read more here.
Keywords: method based; angular motion; motion projectiles; homotopy analysis ... See more keywords