Results 51 to 60 of about 39,585 (286)

Dynamics of the Caputo fractional derivative

Fractional Calculus and Applied Analysis
Abstract In this article we analyse the dynamical behaviour of the Caputo complex fractional derivative. We prove that the Caputo complex fractional derivative operator is Devaney chaotic in the Mittag-Leffler Caputo space. We will also show that a tuple of different iterates of a Caputo derivative multiple is disjoint hypercyclic.
Marina Murillo-Arcila, Alfred Peris, Álvaro Vargas-Moreno   +2 more
openaire   +3 more sources

The general Caputo–Katugampola fractional derivative and numerical approach for solving the fractional differential equations

Alexandria Engineering Journal
In this manuscript, we present the general fractional derivative (FD) along with its fractional integral (FI), specifically the ψ-Caputo–Katugampola fractional derivative (ψ-CKFD).
Lakhlifa Sadek, Sahar Ahmed ldris, Fahd Jarad   +2 more
doaj   +1 more source

Uniqueness for weak solutions of parabolic equations with a fractional time derivative

, 2018
We prove uniqueness for weak solutions to abstract parabolic equations with the fractional Marchaud or Caputo time derivative. We consider weak solutions in time for divergence form equations when the fractional derivative is transferred to the test ...
Allen, Mark
core   +1 more source

Electrical circuits RC and RL involving fractional operators with bi-order

Advances in Mechanical Engineering, 2017
This article describes electrical series circuits RC and RL using the concept of derivative with two fractional orders α and β in Liouville–Caputo sense. The fractional equations consider derivatives in the range of α , β ∈ ( 0 ; 1 ] .
JF Gómez-Aguilar, RF Escobar-Jiménez, VH Olivares-Peregrino, MA Taneco-Hernández, GV Guerrero-Ramírez   +4 more
doaj   +1 more source

New applications of the new general integral transform method with different fractional derivatives

Alexandria Engineering Journal, 2023
Integral transforms are a versatile mathematical technique that can be applied in a wide range of science and engineering fields. We consider the general integral transform with the Caputo derivative and Constant Proportional Caputo derivative in this ...
Ali Akgül, Enver Ülgül, Necibullah Sakar, Büşra Bilgi, Aklime Eker   +4 more
doaj   +1 more source

Towards Fractional Gradient Elasticity

, 2013
An extension of gradient elasticity through the inclusion of spatial derivatives of fractional order to describe power-law type of non-locality is discussed. Two phenomenological possibilities are explored.
Aifantis, Elias C., Tarasov, Vasily E.
core   +1 more source

Numerical approximations for a fully fractional Allen-Cahn equation

, 2020
A finite element scheme for an entirely fractional Allen-Cahn equation with non-smooth initial data is introduced and analyzed. In the proposed nonlocal model, the Caputo fractional in-time derivative and the fractional Laplacian replace the standard ...
Acosta, Gabriel, Bersetche, Francisco
core   +1 more source

Meshless Technique for the Solution of Time-Fractional Partial Differential Equations Having Real-World Applications

Journal of Function Spaces, 2020
In this article, radial basis function collocation scheme is adopted for the numerical solution of fractional partial differential equations. This method is highly demanding because of its meshless nature and ease of implementation in high dimensions and
Mehnaz Shakeel, Iltaf Hussain, Hijaz Ahmad, Imtiaz Ahmad, Phatiphat Thounthong, Ying-Fang Zhang   +5 more
doaj   +1 more source

Operando X‐Ray Diffraction and Total Scattering Characterization of Battery Materials: Not Just a Pretty Picture

Advanced Energy Materials, EarlyView.
This review focuses on operando studies of battery materials by X‐ray diffraction (XRD) and total X‐ray scattering (TXS). This work highlights potential pitfalls and identify best‐practices for operando studies and reviews some unusual experiments to illustrate how these methods can be applied beyond the evaluation of the early‐stage cycling mechanisms
Amalie Skurtveit, Eira Tiberg North, Izar Capel Berdiell, Wouter Van Beek, David S. Wragg, Alexey Y. Koposov   +5 more
wiley   +1 more source

A PRIORI ESTIMATION OF A GENERALIZED NONLOCAL BOUNDARY VALUE PROBLEM FOR A THRID ORDER EQUATION WITH A FRACTIONAL TIME CAPUTO DERIVATIVE [PDF]

Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, 2019
A boundary value problem for a third-order parabolic equation with a fractional Caputo derivative is considered. A priori estimation of the solution of a generalized nonlocal boundary value problem for an equation with multiple characteristics with a ...
A. M. Shkhagapsoev
doaj   +1 more source