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Approximate Solutions to Time-Fractional Schrödinger Equation via Homotopy Analysis Method
We construct the approximate solutions of the time-fractional Schrodinger equations, with zero and nonzero trapping potential, by homotopy analysis method (HAM). The fractional derivatives, in theExpand
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An efficient approach for solving the Riccati equation with fractional orders
The present study introduces a novel and simple analytical method for the solution of fractional order Riccati differential equation. In this approach, the solution considered as a Taylor seriesExpand
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Fractional-order Riccati differential equation: Analytical approximation and numerical results
The aim of this article is to introduce the Laplace-Adomian-Padé method (LAPM) to the Riccati differential equation of fractional order. This method presents accurate and reliable results and has aExpand
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Numerical solutions of time‐fractional Burgers equations
Purpose – The purpose of this paper is to use the generalized differential transform method (GDTM) and homotopy perturbation method (HPM) for solving time‐fractional Burgers and coupled BurgersExpand
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In this work, the homotopy analysis method (HAM) is applied to solve the fourth-order parabolic partial differential equations. This equation practically arises in the transverse vibration problems.Expand
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Radiation effect on boundary layer flow of an Eyring–Powell fluid over an exponentially shrinking sheet
Abstract The aim of this paper was to examine the steady boundary layer flow of an Eyring–Powell model fluid due to an exponentially shrinking sheet. In addition, the heat transfer process in theExpand
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Analytical Study of Navier-Stokes Equation with Fractional Orders Using He's Homotopy Perturbation and Variational Iteration Methods
In the present work, by introducing the fractional derivative in the sense of Caputo, the He's homotopy perturbation method (HPM) and variational iteration method (VIM) are used to study theExpand
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Approximate analytical solutions of fractional reaction-diffusion equations
Abstract The homotopy analysis method (HAM) of S.J. Liao has proven useful in obtaining analytical/numerical solutions to various nonlinear differential equations. In this work, the HAM is employedExpand
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Wavelets optimization method for evaluation of fractional partial differential equations: an application to financial modelling
In the present paper, we employ a wavelets optimization method is employed for the elucidations of fractional partial differential equations of pricing European option accompanied by a Lévy model. WeExpand
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Exact analytic solutions for the unsteady flow of a non-Newtonian fluid between two cylinders with fractional derivative model
The velocity field and the associated shear stress corresponding to the torsional oscillatory flow of a generalized Maxwell fluid, between two infinite coaxial circular cylinders, are determined byExpand
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