An efficient analytical technique for fractional model of vibration equation
TLDR
In this paper, an efficient analytical approach based on the q-homotopy analysis transform technique was presented to analyze a fractional model of the vibration equation for large membranes, and the Laplace decomposition technique was also employed to obtain the solution of the fractional-order vibration equation.About:
This article is published in Applied Mathematical Modelling.The article was published on 2017-05-01 and is currently open access. It has received 177 citations till now. The article focuses on the topics: Laplace's equation & Analytical technique.read more
Citations
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A new fractional exothermic reactions model having constant heat source in porous media with power, exponential and Mittag-Leffler laws
TL;DR: In this paper, the exothermic reactions model with constant heat source in the porous media with strong memory effects is considered and the mathematical equation of the problem is confined in a fractional energy balance equation (FEBE), which furnishes the temperature portrayal in conduction state having uniform heat source on steady state.
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A new study of unreported cases of 2019-nCOV epidemic outbreaks
Wei Gao,Pundikala Veeresha,Haci Mehmet Baskonus,Doddabhadrappla Gowda Prakasha,Pushpendra Kumar +4 more
TL;DR: The epidemic prophecy for the novel coronavirus (2019-nCOV) epidemic in Wuhan, China is studied by using q-homotopy analysis transform method (q-HATM) and the results show that the used scheme is highly emphatic and easy to implementation for the system of nonlinear equations.
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On the analysis of vibration equation involving a fractional derivative with Mittag-Leffler law
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New numerical surfaces to the mathematical model of cancer chemotherapy effect in Caputo fractional derivatives.
TL;DR: The q-homotopy analysis transform method is applied to the mathematical model of the cancer chemotherapy effect in the sense of Caputo fractional to find some new approximate numerical results for different values of parameters of alpha.
References
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Book
An Introduction to the Fractional Calculus and Fractional Differential Equations
Kenneth S. Miller,Bertram Ross +1 more
TL;DR: The Riemann-Liouville Fractional Integral Integral Calculus as discussed by the authors is a fractional integral integral calculus with integral integral components, and the Weyl fractional calculus has integral components.
Book
Beyond Perturbation: Introduction to the Homotopy Analysis Method
Shijun Liao,SA Sherif +1 more
TL;DR: In this paper, a simple bifurcation of a nonlinear problem multiple solutions of a Nonlinear Problem Nonlinear Eigenvalue Problem Thomas-Fermi Atom Model Volterra's Population Model Free Oscillation Systems with Odd Nonlinearity Free oscillations with Quadratic nonlinearity Limit Cycle in a Multidimensional System Blasius' viscous flow Boundary-layer Flow Boundarylayer Flow with Exponential Property Boundary Layer Flow with Algebraic Property Von Karman Swirling Flow Nonlinear Progressive Waves in Deep Water BIBLIOGR
Book
Homotopy Analysis Method in Nonlinear Differential Equations
TL;DR: In this paper, a convergence series for Divergent Taylor Series is proposed to solve nonlinear initial value problems and nonlinear Eigenvalue problems with free or moving boundary in heat transfer.
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