Results 81 to 90 of about 12,535 (181)

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

Application of Newton’s polynomial interpolation scheme for variable order fractional derivative with power-law kernel

Scientific Reports
This paper, offers a new method for simulating variable-order fractional differential operators with numerous types of fractional derivatives, such as the Caputo derivative, the Caputo–Fabrizio derivative, the Atangana–Baleanu fractal and fractional ...
S Naveen, V Parthiban
doaj   +1 more source

Variational Problems Involving a Caputo-Type Fractional Derivative [PDF]

Journal of Optimization Theory and Applications, 2016
The aim of this paper is to study certain problems of calculus of variations, that are dependent upon a Lagrange function on a Caputo-type fractional derivative. This type of fractional operator is a generalization of the Caputo and the Caputo--Hadamard fractional derivatives, that are dependent on a real parameter ro.
openaire   +4 more sources

The Cotangent Derivative with Respect to Another Function: Theory, Methods and Applications

Fractal and Fractional
This paper introduces a generalization of the Riemann–Liouville and Caputo cotangent derivatives and their corresponding integrals, known as the Riemann–Liouville and Caputo cotangent derivatives with respect to another function (RAF).
Lakhlifa Sadek, Ali Algefary
doaj   +1 more source

Asymptotic Integration of Fractional Differential Equations with Integrodifferential Right-Hand Side

Mathematical Modelling and Analysis, 2015
In this paper we deal with the problem of asymptotic integration of a class of fractional differential equations of the Caputo type. The left-hand side of such type of equation is the Caputo derivative of the fractional order r ∈ (n − 1, n) of the ...
Milan Medved, Michal Pospisil
doaj   +1 more source

New Results on Fractional Power Series: Theory and Applications

Entropy, 2013
In this paper, some theorems of the classical power series are generalized for the fractional power series. Some of these theorems are constructed by using Caputo fractional derivatives.
Ahmad El-Ajou, Omar Abu Arqub, Zeyad Al Zhour, Shaher Momani   +3 more
doaj   +1 more source

Fractional Mass-Spring-Damper System Described by Generalized Fractional Order Derivatives

Fractal and Fractional, 2019
This paper proposes novel analytical solutions of the mass-spring-damper systems described by certain generalized fractional derivatives. The Liouville−Caputo left generalized fractional derivative and the left generalized fractional derivative ...
Ndolane Sene, José Francisco Gómez Aguilar   +1 more
doaj   +1 more source

Enhancement in heat transfer due to hybrid nanoparticles in MHD flow of Brinkman-type fluids using Caputo fractional derivatives. [PDF]

Sci Rep, 2022
Sheikh NA, Ching DLC, Khan I, Sakidin HB.   +3 more
europepmc   +1 more source

Author Correction: Enhancement in heat transfer due to hybrid nanoparticles in MHD flow of Brinkman-type fluids using Caputo fractional derivatives. [PDF]

Sci Rep, 2022
Sheikh NA, Ching DLC, Khan I, Sakidin HB.   +3 more
europepmc   +1 more source

Existence and uniqueness of solutions to fractional differential equations in the frame of generalized Caputo fractional derivatives

Advances in Difference Equations, 2018
The generalized Caputo fractional derivative is a name attributed to the Caputo version of the generalized fractional derivative introduced in Jarad et al. (J. Nonlinear Sci. Appl. 10:2607–2619, 2017).
Y. Y. Gambo, R. Ameen, F. Jarad, T. Abdeljawad   +3 more
doaj   +1 more source