The fractional-order approximation
A fractional-order implicit difference approximation for the space-time fractional
... Liouville fractional derivative of order between one and two, and the first order time derivative by a Caputo fractional derivative of order between zero and ...A fractional ...
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Existence and approximation of solutions to fractional order hybrid differential equations
... tan – u n (s) ds (.) for all t ∈ [, ], where u (t) = . for t ∈ [, ]. The iterative sequence for the solution of (.) is numerically illustrated in Figure for the fractional order derivative α ...
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A comprehensive study on different approximation methods of Fractional order system
... different approximation methods are given and these four approximation methods are applied on two different examples and the results are compared both in time domain and in frequency ...a fractional ...
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Fractional order Riccati differential equation: Analytical approximation and numerical results
... Padé approximation; Riccati equation 1 Introduction In recent years, it has turned out that many phenomena in biology, chemistry, acoustics, control theory, psychology and other areas of science can be fruitfully ...
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Approximation at first and second order of m-order integrals of the fractional Brownian motion and of certain semimartingales
... [email protected] and [email protected] Abstract: Let X be the fractional Brownian motion of any Hurst index H ∈ (0, 1) (resp. a semimartingale) and set α = H (resp. α = 1 2 ). If Y is a ...
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Fractional neural network approximation
... continuity Fractional derivative a b s t r a c t Here, we study the univariate fractional quantitative approximation of real valued functions on a compact interval by quasi-interpolation sigmoidal ...
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A numerical study of fractional order reverse osmosis desalination model using Legendre wavelet approximation
... In this study, simulation of small-scale reverse osmosis desalination problem was conducted using a new fractional model. Numerical method of Legendre wavelets associated with the decoupling and ...
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Operational Matrix Method for the Variable Order Time Fractional Diffusion Equation Using Legendre Polynomials Approximation
... Abstract — In this paper, a numerical method based on Legendre polynomials is proposed for solving the variable order time fractional diffusion equation. We adopt the Coimbra variable order time ...
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Finite Element Approximation for the Fractional Eigenvalue Problem
... λ (k) h = λ (k) + Ch α . This allows to extrapolate approximations of the eigenvalues as well (in the tables we denote this extrapolated value of λ (k) as λ (k) ext ). Throughout this section, the results are compared ...
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A fractional type of the Chebyshev polynomials for approximation of solution of linear fractional differential equations
... of fractional derivative of order γ in the Caputo for FCSs and show that this matrix with the Tau method are utilized to reduce the solution of some fractional -order differential ...
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A fractional spline collocation method for the fractional order logistic equation
... Figure 3 displays the numerical solution and the error obtained by using the frac- tional B-splines B α with α = 3, 3.25, 3.5, 3.75, 4, for the two values γ = 1/4 and γ = 1 (Malthus model). These simple tests show that ...
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Sums of reciprocals of fractional parts and multiplicative Diophantine approximation
... n=1 Ψ γ α (n). Note that in this case (9.2) holds for all sufficiently large n and thus our above argument is justified. In order to prove Theorem 2.3 we will have to ensure that the sum (9.3) di- verges. However, ...
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Electronic realization of the fractional-order systems
... the fractional-order systems – controllers or controlled objects whose we earlier used, identified, and analyzed as a mathematical models only – namely a fractional-order differential ...
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Controller Design for Fractional-Order Systems
... of fractional derivatives has become quite apparent in modeling mechanical and electrical properties of real ...materials. Fractional integrals and derivatives has found wide application in the control of ...
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Control Chaos in System with Fractional Order
... 2. Fractional Derivative and Numerical Algorithm There are two approximation methods for solving frac- tional differential ...Caputo fractional derivative defined in [13] is often described ...
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On Fractional Order Influenza A Epidemic Model
... the fractional order differential equations do not have exact analytic solutions, so approximation and numerical techniques must be ...the fractional order differential ...
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Quantitative approximation by fractional smooth Poisson Cauchy singular operators
... general fractional smooth Poisson Cauchy singular integral operators on the real line, regarding their convergence to the unit operator with fractional rates in the uniform ...higher order moduli of ...
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Implicit difference approximation of the Galilei invariant fractional advection diffusion
... Physical conditions impose the range 0 < γ < 1 . In this example we select three typical values γ = 0.4 , 0.5 and 0.6 in this range. Our analysis indicates a convergence order of O(τ + h 2 ) for small τ and ...
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Error analysis of an explicit finite difference approximation for the space fractional
... ANZIAM J. 46 (E) pp.C871–C887, 2005 C872 for sfde with insulated ends is discussed. We derive the scaling re- striction of the stability and convergence of the explicit numerical method. Finally, some numerical results ...
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Fractional-order functions for solving fractional-order variational problems with boundary conditions
... the fractional-order variational problems (FVPs) with boundary conditions is ...The fractional derivative in the problem is in the Caputo ...using fractional-order Bernoulli functions ...
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