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11.03.2012 · In [18, 19], the Riesz Riemann-Liouville fractional derivative or simply the Riesz fractional derivative and the Caputo Riesz fractional derivative are, respectively, represented as In [ 1 ], a formula for the fractional integration by parts on the whole interval was given by the following lemma.

... representations of the Riesz derivative, which plays an important role in anomalous diffusion and space fractional quantum mechanics.

As described by Wheatcraft and Meerschaert (2008), a fractional conservation of mass equation is needed to model fluid flow when the control volume is not large enough compared to the scale of heterogeneity and when the flux within the control volume is non-linear. In the referenced paper, the fractional conservation of mass equation for fluid flow is: When studying the redox behavior of a substrate in solution, a voltage is applied at an electrode …

We consider the solvability of fractional differential equations involving the Riesz fractional derivative. Our approach basically relies on ...

The Fourier transform method is used to solve fractional Poisson’s equation with Riesz fractional derivative of order α. It is shown that the solution is given in terms of the fractional ...

Keywords: fractional Laplacian, fractional derivative, Riesz potential, Green second identity, hyper-singularity, boundary conditions 1. Introduction The fractional Laplacian and the fractional derivative are two different mathematical concepts (Samko et al, 1987). Both are defined through a singular convolution

01.08.2019 · If the Riesz fractional derivative variation strategy of the t th iteration is not improved for the optimal individual in Fig. 10, the distance of the t th iteration is zero. From Fig. 9 it can be seen that the update of the optimal individual is frequent, which proves the validity of the Riesz fractional derivative mutation strategy.

fractional Riesz and fractional Riesz–Caputo derivatives as [4] the Riesz fractional derivative (RFD) R a D α t x(t)= 1 (n −α) d dt n b a |t −τ|n−α−1x(τ)dτ = DnR a I (10) = || = = + and = + (). = =.

for α > 0. 2.2.1.4 Riesz Fractional Integrals. Riemann-Liouville and Weyl fractional integrals have upper or lower limits of integration ...

Analytical approximation of time-fractional telegraph equation with Riesz space-fractional derivative · DOI · Find all available articles from these authors · Find ...

04.08.2016 · Generalizations of fractional derivatives of noninteger orders for N-dimensional Euclidean space are proposed. These fractional derivatives of the Riesz type can be considered as partial derivatives of noninteger orders. In contrast to the usual Riesz derivatives, the suggested derivatives give the usual partial derivatives for integer values of orders. For integer …

Partial fractional derivatives of Riesz type and nonlinear fractional differential equations. Vasily E. Tarasov. Received: 15 July 2015 / Accepted: 27 July ...

Fractional variational calculus in terms of Riesz fractional derivatives 6289 In this paper, we develop the GELEs and the transversality conditions for FVPs defined in terms of Riesz fractional derivatives (RFDs). Thus, it extends the FCV available to researchers so far. Definition of a Riesz fractional potential is used to define an RFD.

... The Riesz fractional derivative (RFD) naturally lends itself in diffusion phenomena, because it corresponds to Laplacian in arbitrary dimensions [8]. Some ...

Fractional calculus is a branch of mathematical analysis that studies the several different ... 7.4 Atangana-Baleanu fractional derivative; 7.5 Riesz derivative ...

The Riesz fractional derivative a R D b α y is given by a R D b α y ( x ) = 1 2 ( a D x α y ( x ) − x D b α y ( x ) ) . The left and right Caputo fractional ...

Oct 01, 2019 · DFrFT has been used in the various applications of signal and image processing such as filtering, edge detection, pattern recognition, image compression, etc. [18], [21], [37]. The Riesz fractional order derivative of a discrete domain signal is obtained using the DFrFT presented in [37].

Fractional derivatives have been successfully applied in modeling numerous prob- lems in different fields of applied science. This is because the hereditary ...

Aug 01, 2019 · The Riesz fractional derivative is defined as follows. Definition. Let function g x be continuous in interval 0, x. Divide the interval 0, x into M equal parts and the step length h = x M. The approximate formula for the α order Riesz fractional derivative of g x with second-order accuracy is as follows.

with symmetric Riesz-Caputo fractional derivative using hybrid radial basis function pseu- dospectral where the fractional differentiation matrices are used ...

Aug 04, 2016 · The partial fractional derivatives of the Riesz type of orders \alpha for integer positive values \alpha =m \in \mathbb {N} are usual partial derivative of integer orders m, \begin {aligned} \mathbb {D} {m\brack j} \, f (\mathbf {r}) = \frac {\partial ^ {m} f (\mathbf {r})} {\partial x_j^ {m} } , \end {aligned} (25)

22.05.2014 · The Riesz fractional derivative was derived from the kinetics of chaotic dynamics [14, 15]. For the Riesz fractional differential equations, there have existed several analytical and numerical methods. Zhang and Liu studied the analytical solutions of space Riesz and time Caputo fractional partial differential equations.

03.08.2020 · The article investigates a Riesz–Feller space-fractional backward diffusion problem. We develop a generalized Tikhonov regularization method to overcome the ill-posedness of this problem, and then based on the result of conditional stability, we derive the convergence estimates of logarithmic and double logarithmic types for the regularized method by adopting …

The Fourier transform method is used to solve fractional Poisson’s equation with Riesz fractional derivative of order α. It is shown that the solution is given in …

19.02.2019 · Moreover, if \(\lambda=0\), then the Riesz tempered fractional derivative will reduce to the usual Riesz fractional derivative (see e.g. [3,4,5,6,7,8]). In recent years, differential equations with tempered fractional derivatives have widely been used for modeling many special phenomena, such as geophysics [9,10,11] and finance [12, 13] and so on.

May 22, 2014 · The Riesz fractional derivative was derived from the kinetics of chaotic dynamics [14, 15]. For the Riesz fractional differential equations, there have existed several analytical and numerical methods. Zhang and Liu studied the analytical solutions of space Riesz and time Caputo fractional partial differential equations.