On analytical solution of system of nonlinear fractional boundary value problems associated with obstacle

Waheed, Abdul; Mohyud‐Din, Syed Tauseef; Naz, Iqra

doi:10.1016/j.joes.2017.12.001

Cited by 4 publications

(1 citation statement)

References 14 publications

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“…the simplified Hirota's technique [24], The Wentzel-Kramers-Brillouin asymptotic method [25], Darboux transformation [26], the conformable sub-equation method [27], the improved system technique [28], the modified extended direct algebraic method [29], the linear superposition principle [30], tanh-sech method and modified Kudryashov method [31], the two variable (G'/G, 1/G)-expansion [32], a variation of parameters method (VPM) and Adomian's decomposition method (ADM) [33], the invariant subspace scheme [34], q-homotopy analysis method and Sumudu transform [35], modified versions of variational iteration algorithms [36], the standard B-spline collocation method [37] and well-known many others.…”

Section: Introductionmentioning

confidence: 99%

On the soliton solutions to some system of complex coupled nonlinear models and the effect of the coupling coefficients

Ozisik,

Esen,

Secer

et al. 2024

Preprint

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In this work, we take into account the (2 + 1)-Davey Stewartson equation (DSE) and (2 + 1)-Complex Coupled Maccari System (CCMS) and their analytical solutions. Besides, we tackle with the role of the problem parameters on the soliton behavior which the investigated DSE produces. Exact traveling wave solutions are highly useful in numerical and analytical theories in such equations. We use an efficient analytical approach to calculate the soliton solutions of these models. We have shown that soliton solutions’ features can represent the spread of propagation on the wave fronts and show a reasonable dependency on parameter values. Some of the solutions discovered in three and two-dimensional arrangements can also be described in graphic representations for their behavior. The results show that the technique is easy applicable, efficient, reliable, robust and categorical when it comes to find exact solutions for different nonlinear models. Moreover, the problem parameters and the coupling coefficients have significant effects on the behavior of the solitons of the DSE and this examination is studied for the first time in this article.

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Section: Introductionmentioning

confidence: 99%

On the soliton solutions to some system of complex coupled nonlinear models and the effect of the coupling coefficients

Ozisik,

Esen,

Secer

et al. 2024

Preprint

View full text Add to dashboard Cite

show abstract

On the soliton solutions to some system of complex coupled nonlinear models and the effect of the coupling coefficients

Ozisik,

Esen,

Secer

et al. 2024

Opt Quant Electron

View full text Add to dashboard Cite

In this work, we take into account the (2+1)-Davey Stewartson equation (DSE) and the (2+1)-complex coupled Maccari system (CCMS) and their analytical solutions. Besides, we tackle the role of the problem parameters on the soliton behavior produced by the presented DSE. Exact traveling wave solutions are highly useful in numerical and analytical theories for such equations. While numerical methods are widely used, improving analytical approaches for obtaining analytical solutions is necessary for a deeper understanding of dynamics. This study marks a significant milestone by implementing the efficient analytical approach, enhanced modified extended tanh expansion method, for the first time to the (2+1)-DSE and (2+1)-CCMS equations, thereby making a notable contribution to the existing literature. We have shown that features of the soliton solutions can represent the spread of propagation on the wavefronts and show a reasonable dependency on parameter values. Some of the solutions discovered in three- and two-dimensional arrangements can also be described in graphic representations of their behavior. With the help of the graphical depictions, bright, singular, and periodic singular soliton characters for the $$(2+1)$$ ( 2 + 1 ) -DSE and singular, dark, bright, and periodic singular soliton characters for the $$(2+1)$$ ( 2 + 1 ) -CCMS are acquired. The results show that the utilized analytical technique is easily applicable, efficient, reliable, robust, and categorical when it comes to finding analytical solutions for different nonlinear models. Moreover, the problem parameters and the coupling coefficients have significant influences on the behavior of the solitons of the DSE, and this examination is studied for the first time in this article.

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Efficient analytical approach to solve system of BVPs associated with fractional obstacle problem

et al. 2019

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The general obstacle framework has found applications in steady state fluid interaction, thin-plate fluid dynamics, study of minimal surfaces, control theory, elasto-statics, etc. The obstacle problem involving the fractional operator indeed appears in many contexts, such as in the analysis of anomalous diffusion, in the quasi-geostrophic flow problem, and in pricing of American options regulated by assets evolving in relation to jump processes; these notable applications in financial mathematics and physics made the obstacle problem very important in recent times. In this work, we present a fractional contact problem in which derivative of fractional order in the sense of Caputo is involved. Using the penalty function method, we degenerate it into a system of fractional boundary value problems with known obstacle. We apply the variational iteration method (VIM) for finding the series solution of these fractional BVPs. In order to ensure the accuracy and convergence of solution, residual errors of the solutions for various values of fractional parameters are plotted. The quite accurate results show that variational iteration method is one of the highly potential and robust method for solving fractional BVPs.

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On analytical solution of system of nonlinear fractional boundary value problems associated with obstacle

Cited by 4 publications

References 14 publications

On the soliton solutions to some system of complex coupled nonlinear models and the effect of the coupling coefficients

On the soliton solutions to some system of complex coupled nonlinear models and the effect of the coupling coefficients

On the soliton solutions to some system of complex coupled nonlinear models and the effect of the coupling coefficients

Efficient analytical approach to solve system of BVPs associated with fractional obstacle problem

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