Results 51 to 60 of about 1,816,969 (371)

Non-local fractional derivatives. Discrete and continuous [PDF]

, 2016
We prove maximum and comparison principles for fractional discrete derivatives in the integers. Regularity results when the space is a mesh of length $h$, and approximation theorems to the continuous fractional derivatives are shown.
0000-0002-8112-0180, Abadias, Luciano, De León-Contreras, Marta, Torrea, José L.   +3 more
core   +3 more sources

A modified invariant subspace method for solving partial differential equations with non-singular kernel fractional derivatives

, 2020
In this work, the well known invariant subspace method has been modified and extended to solve some partial differential equations involving Caputo-Fabrizio (CF) or Atangana-Baleanu (AB) fractional derivatives. The exact solutions are obtained by solving
Kamal Ait Touchent, Z. Hammouch, T. Mekkaoui   +2 more
semanticscholar   +1 more source

Fractional Liouville Equation on Lattice Phase-Space

, 2015
In this paper we propose a lattice analog of phase-space fractional Liouville equation. The Liouville equation for phase-space lattice with long-range jumps of power-law types is suggested.
Tarasov, Vasily E.
core   +1 more source

Fractional integrals and derivatives: mapping properties [PDF]

, 2016
This survey is aimed at the audience of readers interested in the information on mapping properties of various forms of fractional integration operators, including multidimensional ones, in a large scale of various known function spaces.As is well known,
Rafeiro, Humberto, Samko, Stefan
core   +1 more source

A Fractional Calculus of Variations for Multiple Integrals with Application to Vibrating String [PDF]

, 2010
We introduce a fractional theory of the calculus of variations for multiple integrals. Our approach uses the recent notions of Riemann-Liouville fractional derivatives and integrals in the sense of Jumarie. Main results provide fractional versions of the
Almeida, Ricardo, Malinowska, Agnieszka B., Torres, Delfim F. M.   +2 more
core   +4 more sources

A New Mixed Fractional Derivative with Applications in Computational Biology

Computation
This study develops a new definition of a fractional derivative that mixes the definitions of fractional derivatives with singular and non-singular kernels.
Khalid Hattaf
doaj   +1 more source

Lyapunov-type inequalities for fractional differential equations: a survey [PDF]

Surveys in Mathematics and its Applications, 2021
A survey of results on Lyapunov-type inequalities for fractional differential equations associated with a variety of boundary conditions is presented.
Sotiris K. Ntouyas, Bashir Ahmad
doaj  

FRACTIONAL CENTRAL DIFFERENCES AND DERIVATIVES [PDF]

IFAC Proceedings Volumes, 2006
Fractional central differences and derivatives are studied in this article. These are generalisations to real orders of the ordinary positive (even and odd) integer order differences and derivatives, and also coincide with the well known Riesz potentials.
openaire   +2 more sources

Inequalities for Riemann–Liouville-Type Fractional Derivatives of Convex Lyapunov Functions and Applications to Stability Theory

Mathematics, 2023
In recent years, various qualitative investigations of the properties of differential equations with different types of generalizations of Riemann–Liouville fractional derivatives were studied and stability properties were investigated, usually using ...
Ravi P. Agarwal, Snezhana Hristova, Donal O’Regan   +2 more
doaj   +1 more source

Desiderata for Fractional Derivatives and Integrals

Mathematics, 2019
The purpose of this brief article is to initiate discussions in this special issue by proposing desiderata for calling an operator a fractional derivative or a fractional integral.
R. Hilfer, Yuri Luchko
semanticscholar   +1 more source