Fractional derivatives are applied in the reconstruction, from a single observable, of the dynamics of a Duffing oscillator and a two-well experiment. The fractional derivatives of time series data are obtained in the frequency domain. The derivative fraction is evaluated using the average mutual information between the observable and its fractional derivative. The ability of this reconstructio...

In this paper, we analyze the spectra of preconditioned matrices arising from discretized multi-dimensional Riesz spatial fractional diffusion equations. The finite difference method is employed to approximate derivatives, which will generate symmetric positive definite ill-conditioned multi-level Toeplitz matrices. conjugate gradient with a preconditioner based on sine transform solve resultin...

Translation and convolution associated with discrete wavelet transform are investigated using properties of Calderón-Zygmund operator and Riesz fractional integral operator. Dual convolution is also studied. The wavelet convolution is applied to approximate functions belonging to certain p L-spaces.

In this paper we present a comprehensive treatment of function spaces with logarithmic smoothness (Besov, Sobolev, Triebel-Lizorkin). We establish the following results: Sharp embeddings between Besov defined by differences and Fourier-analytical decompositions as well Sobolev/Triebel-Lizorkin spaces; Various new characterizations for norms in terms different K-functionals. For instance, derive...

In the paper, we extend the differential transform method to solve nonlinear fractional partial differential equations. The timeand space-fractional Burgers equations with initial conditions are chosen to illustrate our method. As a result, we successfully obtain some available approximate solutions of them. The results reveal that the proposed method is very effective and simple for obtaining ...

Starting from the pseudo-differential decomposition D = ( − Δ ) 1 2 H of Dirac operator ∑ j n e ∂ x in terms fractional order and Riesz–Hilbert type we will investigate fundamental solutions space-fractional equation Lévy–Feller t Φ α , ; θ exp i π involving Laplacian α, with 2m≤α < 2m + m ∈ ℕ), exponentiation as hypercomplex counterpart transform carrying skewness parameter θ, values range | ≤...

The paper presents a new fractional integration, which generalizes the Riemann-Liouville and Hadamard fractional integrals into a single form, which when a parameter fixed at different values, produces the above integrals as special cases. Conditions are given for such a generalized fractional integration operator to be bounded in an extended Lebesgue measurable space. Semigroup property for th...

We introduce Riesz Logic, whose models are abelian lattice ordered groups, which generalise Riesz spaces (vector lattices), and show soundness and completeness. Our motivation is to provide a logic for distributional semantics of natural language, where words are typically represented as elements of a vector space whose dimensions correspond to contexts in which words may occur. This basis prov...

in the present paper, we introduce some new sequence spaces derived by riesz mean and the notions of almost and strongly almost convergence in a real 2-normed space. some topological properties of these spaces are investigated. further, new concepts of statistical convergence which will be called weighted almost statistical convergence, almost statistical convergence and statistical convergence...

Here we prove fractional representation formulae involving generalized fractional derivatives, Caputo fractional derivatives and Riemann–Liouville fractional derivatives. Then we establish Poincaré, Sobolev, Hilbert–Pachpatte and Opial type fractional inequalities, involving the right versions of the abovementioned fractional derivatives.