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Algorithms for the fractional calculus: A selection of numerical methods
Computational method for a fractional model of the helium
Numerical Methods for the Fractional Laplacian: A Finite Difference
Two New Implicit Numerical Methods for the Fractional Cable
COMPUTATIONAL METHODS FOR THE FRACTIONAL OPTIMAL
A new and efficient numerical method for the fractional modeling
A Computational Method for the Time-Fractional Navier-Stokes
On numerical techniques for solving the fractional logistic differential
Numerical methods for the solution of partial differential equations of
Comparison of computational methods for the identification of cell
A class of shifted high-order numerical methods for the fractional
SM-Algorithms for Approximating the Variable-Order Fractional
Operational Methods in the Study of Sobolev-Jacobi Polynomials
An efficient computational method based on the hat functions
Spectral Method for the Fractional Laplacian in 2D and
Impact of Side Branches on the Computation of Fractional Flow
Numerical experiments are pro-vided to illustrate potential and limitations of the di erent methods under investigation. Keywords: fractional di erential equations, multistep methods, trapezoidal method, convergence, stability, computational aspects.
In this paper, an efficient and accurate computational method based on the hat functions (hfs) is proposed for solving a class of fractional optimal control problems (focps). In the proposed method, the fractional optimal control problem under consideration is reduced to a system of nonlinear algebraic equations which can be simply solved.
In this paper, we present new ideas for the implementation of homotopy asymptotic method (ham) to solve systems of nonlinear fractional differential equations (fdes). An effective computational algorithm, which is based on taylor series approximations of the nonlinear equations, is introduced to accelerate the convergence of series solutions.
(2011) high-order finite element methods for time-fractional partial di_erential equations. Journal of computational and applied mathematics, 235, 3285-3290.
The results prove that the proposed method is very effective and simple for solving fractional partial differential equations.
This book fills a gap in the literature by introducing numerical techniques to solve problems of fractional calculus of variations (fcv).
Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives.
Numerical methods for fractional calculus presents numerical methods for fractional integrals and fractional derivatives, finite difference methods for fractional ordinary differential equations (fodes) and fractional partial differential equations (fpdes), and finite element methods for fpdes.
In this work, we introduce a useful and efficient calculation method for solving a new computational method based on fractional lagrange functions to solve.
Because of the lack of analytic methods to solve such fractional problems, numerical techniques are developed.
To further minimize the computational cost of the simulation-based entropy method, a multiplicative dimensional reduction method (m-drm) was proposed to compute the fractional (integer) moments of a generic function with multiple input variables.
Background: computational fluid dynamics (cfd) allows noninvasive fractional flow (ff) computation in intracranial arterial stenosis. Removal of small artery branches is necessary in cfd simulation. Methods: an idealized vascular model was built with 70% focal luminal stenosis.
Numerical methods for fractional calculus presents numerical methods for fractional integrals and fractional derivatives, finite difference methods for fraction.
Computational methods for differential equations (cmde) and petrov-galerkin method for solving fractional volterra-fredholm integro-differential equations.
Hereafter, a suitable method, that can be found in the classical literature, is employed to find an approximate solution for the original fractional problem. Here we focus mainly on the left derivatives and the details of extracting corresponding expansions. Right derivatives are given whenever it is needed to apply new techniques.
Keywords: grunwald–letnikov fractional derivative; mathematical modeling. Non -linear computational methods and numerical simulations successfully.
Sep 9, 2019 section iv suggests a new, efficient numerical method to solve the proposed fractional dynamical system.
Computational method for fractional differential equations using nonpolynomial fractional spline faraidun salh introductionduring the past three decades, fractional differential equation has gained importance due to its applicability in diverse fields of science and engineering, such as, control theory, viscoelasticity, diffusion, neurology.
Computational methods for fractional-order problems bari, italy, july 22-26, 2019 a large extent of systems in biology, economics, engineering, physics, and other areas, are modeled by means of differential equations of fractional order whose correct treatment requires the attainment of advanced skills for numerical simulations.
Computational methods for the fractional optimal control hiv infection lf abd elal, nh sweilam, am nagy, ys almaghrebi journal of fractional calculus and applications 7 (2), 121-131 2016.
This book discusses numerical methods for solving partial differential and integral equations, fractional calculus can be classified as applicable mathematics.
Jun 21, 2018 computation, on thursday, june 21, 2018 on the topic: anomalous infiltration into heterogeneous porous media: simulations and fractional.
Get this from a library! fractional calculus models and numerical methods. [d baleanu;] -- this book will give readers the possibility of finding very important.
This 4th edition of the classic textbook offers an overview of techniques used to solve problems in fluid mechanics on computers. Direct and large-eddy simulation of turbulence, multigrid methods, parallel computing, moving grids, structured boundary-fitted grids, free surface flows.
The purpose of this paper is to apply an efficient hybrid computational numerical technique, namely, q-homotopy analysis sumudu transform method (q-hastm) and residual power series method (rpsm) for finding the analytical solution of the non-linear time-fractional hirota–satsuma coupled kdv (hs-ckdv) equations.
In this article, we apply the generalized bdf2-θ to the fractional mobile/immobile transport equations for its temporal discretization and the finite element method.
Dec 14, 2013 because of the lack of analytic methods to solve such fractional problems, numerical techniques are developed.
Computational methods for fractional-order problems a large extent of systems in biology, economics, engineering, physics, and other areas, are modeled by means of differential equations of fractional order whose correct treatment requires the attainment of advanced skills for numerical simulations.
Anomalous diffusion is a possible mechanism underlying plasma transport in magnetically confined plasmas.
Nov 30, 2020 partial differential equations (pdes) are used with huge success to model phenomena across all scientific and engineering disciplines.
The system of fractional differential equations is solved simultaneously using series expansion method. The calculations are performed in the sense of modified riemann–liouville fractional derivative. Analytic expressions are obtained for the abundance of each element as a function of time.
Aug 28, 2020 homotopy transforms analysis method for solving fractional navier- stokes equations of fractional order derivative, numerical solution.
Recent efforts for fractional order identification have mainly focused on time-fractional advection-dispersionequations (ades) [4–9]and, to a lesser extent, on parameter identification of the space-fractional ades but only limited to constant fractional order [10–12].
In particular, the development of numerical software for the effective treatment of fractional-order systems.
These methods are an extension of the weighted average methods for ordinary (non-fractional) diffusion equations. Their accuracy is of order (δx)2 and δt, except for the fractional version of the crank-nicholson method, where the accuracy with respect to the timestep is of order (δt)2 if a second-order approximation to the fractional time.
The fractional calculus of variations and fractional optimal control are generalizations of the corresponding classical theories, that allow problem modeling and formulations with arbitrary order derivatives and integrals. Because of the lack of analytic methods to solve such fractional problems, numerical techniques are developed. Here, we mainly investigate the approximation of fractional.
The fractional calculus can be obtained either from the generalization of the definition of the derivative or the definition of the integral. Depending on the type of approach selected, the resulting mathematical equation is different. If the extension is build from the derivative, then the grünwald–letkikov method is obtained.
Here, we provide the first benchmark of these computational methods by comparing and because b1 was explicitly removed, a relatively small fraction of these.
The computational complexities of time fractional, space fractional, and space-time fractional equations are o (n2m), o (nm2), and o (nm (m + n)) compared with o (mn) for the classical partial differential equations with finite difference methods, where m, n are the number of space grid points and time steps.
The main purpose of this paper is to present a new computational for approximate analytical solutions of nonlinear time-fractional wave-like equations with variable coefficients using the fractional residual power series method (frpsm).
Further, the nature of the solution is captured for different value of the fractional order. The comparison study has been performed to verify the accuracy of the future algorithm. The achieved results illuminate that, the suggested computational method is very effective to investigate the considered fractional-order model.
The paper describes different approaches to generalize the trapezoidal method to fractional differential equations. We analyze the main theoretical properties and we discuss computational aspects to implement efficient algorithms. Numerical experiments are provided to illustrate potential and limitations of the different methods under.
This paper explores a new method, called fractional pseudospectral method (fpm), which solves the linear and nonlinear fractional ordinary/partial differential equations (fodes/fpdes).
Jan 1, 2019 of series manipulations for computing lacunary generating functions, our main application of these techniques is the study of sobolev-jacobi.
Spectral method for the fractional laplacian in 2d and 3d kailai xua, eric darveb ainstitute for computational and mathematical engineering, stanford university, stanford, ca, 94305 bmechanical engineering, stanford university, stanford, ca, 94305 abstract a spectral method is considered for approximating the fractional laplacian.
A computational method for the time-fractional navier-stokes equation abstract: in this study, navier-stokes equations with fractional derivate are solved according to time variable. To solve these equations, hybrid generalized differential transformation and finite difference methods are used in various subdomains.
A numerical method for the fractional laplacian is proposed, based on the singular integral representation for the operator.
This unique fusion of old and new leads to a unified approach that intuitively parallels the classic theory of differential equations, and results in methods that are unprecedented in computational speed and numerical accuracy. The opening chapter is an introduction to fractional calculus that is geared towards scientists and engineers.
A numerical method for the fractional laplacian is proposed, based on the singular integral representation for the operator. The method combines finite differences with numerical quadrature to obtain a discrete convolution operator with positive weights.
Mar 2, 2020 in this paper we try to identify some common pitfalls in the use of numerical methods in fractional calculus, to explain their nature and to list.
May 12, 2020 in this work, we derived a novel numerical scheme to find out the numerical solution of fractional pdes having caputo-fabrizio (c-f) fractional.
Moreover, they employed these fractional bases to introduce a new class of fractional interpolants to develop efficient and spectrally accurate collocation methods in [46] for a variety of fodes and fpdes including multi-term fpdes and the nonlinear space-fractional burgers’ equation.
Mar 11, 2017 fractional calculus, variable-order derivative, spline approximation, finite difference approximation, convergence order, numerical method.
Our numerical methods for problems described by fractional-order derivatives, integrals, and differential equations.
Computational methods in the fractional calculus of variations kindle edition by ricardo almeida (author), shakoor pooseh (author), delfim f m torres (author).
The solution of fractional-order differential problems requires in the majority of cases the use of some computational approach.
Research interests: partial differential equations and harmonic analysis. Nonlocal equations; fractional derivatives; fractional laplacians; regularity theory.
In this paper two numerical methods are used to study the non- linear fractional optimal control problem (focp) for the human immunodefi- ciency virus (hiv).
Numerical methods to solve the problems are presented, and some computational simulations are discussed in detail (pooseh, almeida and torres, 2014). No access chapter 11: an expansion formula for fractional operators of variable order.
Novel methods in computational finance, including fractional black-scholes equation, fractional diffusion models of option prices in markets with jumps, stock exchange fractional dynamics, option pricing of a bi-fractional black-merton-scholes model, tempered fractional black-scholes model for european double barrier option.
Computational methods in the fractional calculus of variations - kindle edition by ricardo almeida, shakoor pooseh, delfim f m torres.
Li’s main research interests include numerical methods and computations for fpdes and fractional dynamics.
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