Fractional Lienard Type Model of a Pipeline Within the Fractional Derivative Without Singular Kernel
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Date
2016
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Springeropen
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GOLD
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Abstract
This paper presents the procedure to obtain analytical solutions of Li,nard type model of a fluid transmission line represented by the Caputo-Fabrizio fractional operator. For such a model, we derive a new approximated analytical solution by using the Laplace homotopy analysis method. Both the efficiency and the accuracy of the method are verified by comparing the obtained solutions with the exact analytical solution. Good agreement between them is confirmed.
Description
Gomez-Aguilar, J.F./0000-0001-9403-3767; Yepez-Martinez, Huitzilin/0000-0002-8532-5669; Torres, Lizeth/0000-0002-4937-4586
Keywords
Pipelines, Fluid Dynamics, Nonlinear Oscillators, Lienard Equation, Laplace Homotopy Analysis Method, Fractional Differential Coupled Equation, Financial economics, Laplace transform, Economics, Operator (biology), Mathematical analysis, Biochemistry, Gene, Convergence Analysis of Iterative Methods for Nonlinear Equations, Engineering, Differential equation, FOS: Mathematics, Biology, Anomalous Diffusion Modeling and Analysis, Numerical Analysis, Algebra and Number Theory, Ecology, Applied Mathematics, Fractional calculus, Pure mathematics, Partial differential equation, Derivative-Free Methods, Applied mathematics, Fracture Mechanics Modeling and Simulation, Fractional Derivatives, Homotopy analysis method, Chemistry, Mechanics of Materials, Modeling and Simulation, Derivative (finance), FOS: Biological sciences, Physical Sciences, Kernel (algebra), Repressor, Fractional Calculus, Homotopy Analysis Method, Homotopy, Transcription factor, Type (biology), Analysis, Mathematics, Ordinary differential equation, Fractional ordinary differential equations, fluid dynamics, Fractional derivatives and integrals, pipelines, fractional differential coupled equation, nonlinear oscillators, PDEs in connection with fluid mechanics, Liénard equation, Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems, Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc., Laplace homotopy analysis method, Fractional partial differential equations
Turkish CoHE Thesis Center URL
Fields of Science
0211 other engineering and technologies, 02 engineering and technology, 0203 mechanical engineering
Citation
Gomez-Aguilar, J. F...et al. (2016). Fractional Lienard type model of a pipeline within the fractional derivative without singular kernel. Advance in Difference Equations. http://dx.doi.org/10.1186/s13662-016-0908-1
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Q1
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OpenCitations Citation Count
69
Source
Advances in Difference Equations
Volume
2016
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CrossRef : 49
Scopus : 92
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Mendeley Readers : 13
SCOPUS™ Citations
91
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Web of Science™ Citations
69
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Page Views
2
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10.94731077
Sustainable Development Goals
7
AFFORDABLE AND CLEAN ENERGY
9
INDUSTRY, INNOVATION AND INFRASTRUCTURE
10
REDUCED INEQUALITIES
11
SUSTAINABLE CITIES AND COMMUNITIES
