Results 261 to 270 of about 755,580 (294)

Method for defining a class of fractional operations

IEEE Transactions on Signal Processing, 1998
Summary: The fractional Fourier transform (FRT) permits a variety of associated fractional operations. This correspondence proposes a systematic method, based on the structure of the FRT, which not only provides unambiguous extensions of ordinary operations but permits writing the applicable expressions simply by inspection.
P. KRANIAUSKAS, CARIOLARO, GIANFRANCO, ERSEGHE, TOMASO   +2 more
openaire   +3 more sources

On adjoint operators for fractional differentiation operators

Russian Universities Reports. Mathematics, 2020
On a linear manifold of the space of square summable functions on a finite segment vanishing at its ends, we consider the operator of left-sided Caputo fractional differentiation. We prove that the adjoint for it is the operator of right-sided Caputo fractional differentiation.
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Operational methods, fractional operators and special polynomials

Applied Mathematics and Computation, 2003
The paper is devoted to application of fractional powers of operators to special functions and operator-differential equations. Using the operator formula \[ a^{-\nu}={\frac{1}{\Gamma (\nu)}}\int^{\infty}_{0}\exp (-at)t^{\nu -1}dt,\eqno(1) \] the author discusses a formal representation of \(a^{-\nu}f(x)\) with partial differential operators \(a\) as ...
openaire   +3 more sources

Mikusiński’s operational calculus for multi-dimensional fractional operators with applications to fractional PDEs

Communications in Nonlinear Science and Numerical Simulation
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Noosheza Rani, Arran Fernandez
openaire   +3 more sources

Fractional Number Operator and Associated Fractional Diffusion Equations

Mathematical Physics, Analysis and Geometry, 2017
The author studies the fractional number operator as an analog of the finite-dimensional fractional Laplacian and gives a relation with the Ornstein-Uhlenbeck process. Using a semigroup approach, the solution of the Cauchy problem associated to the fractional number operator is presented.
openaire   +1 more source

Fractional calculus and fractional order operators

2015
Fractional order differential equations are an efficient tool to model various processes arising in science and engineering. Fractional models adequately reflect subtle internal properties, such as memory or hereditary properties, of complex processes that the classical integer order models neglect.
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Numbers and Operations – Fractions

2014
In this chapter, you will deal with content-practice, teaching, and learning issues relevant to fractions and operations in the Numbers and Operations –Fractions (NF) domain from Grades 1 through 5 of the CCSSM.
openaire   +1 more source

Fractional Diffusion Equation With New Fractional Operator

AEJ - Alexandria Engineering Journal, 2020
Ndolane Sene
exaly  

A Review of Definitions of Fractional Derivatives and Other Operators

Journal of Computational Physics, 2019
José António Tenreiro Machado, E Capelas de Oliveira   +1 more
exaly  

Variable Order and Distributed Order Fractional Operators

Nonlinear Dynamics, 2002
Tom T Hartley, Carl F Lorenzo
exaly