Results 11 to 20 of about 29,026 (312)

Approximation of the Riesz–Caputo Derivative by Cubic Splines

Algorithms, 2022
Differential problems with the Riesz derivative in space are widely used to model anomalous diffusion. Although the Riesz–Caputo derivative is more suitable for modeling real phenomena, there are few examples in literature where numerical methods are ...
Francesca Pitolli, Chiara Sorgentone, Enza Pellegrino   +2 more
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On Riemann‐Liouville and Caputo Derivatives [PDF]

Discrete Dynamics in Nature and Society, 2011
Recently, many models are formulated in terms of fractional derivatives, such as in control processing, viscoelasticity, signal processing, and anomalous diffusion. In the present paper, we further study the important properties of the Riemann‐Liouville (RL) derivative, one of mostly used fractional derivatives.
Changpin Li, Deliang Qian, YangQuan Chen
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Fractional hamilton formalism within caputo’s derivative [PDF]

Czechoslovak Journal of Physics, 2006
In this paper we develop a fractional Hamiltonian formulation for dynamic systems defined in terms of fractional Caputo derivatives. Expressions for fractional canonical momenta and fractional canonical Hamiltonian are given, and a set of fractional Hamiltonian equations are obtained.
Baleanu, Dumitru, Agrawal, Om. P.
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Fractional Telegraph Equation with the Caputo Derivative

Fractal and Fractional, 2023
The Cauchy problem for the telegraph equation (Dtρ)2u(t)+2αDtρu(t)+Au(t)=f(t) (0<t≤T,0<ρ<1, α>0), with the Caputo derivative is considered. Here, A is a selfadjoint positive operator, acting in a Hilbert space, H; Dt is the Caputo fractional derivative.
Ravshan Ashurov, Rajapboy Saparbayev
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Numerical solutions of fractional optimal control with Caputo–Katugampola derivative

Advances in Difference Equations, 2021
In this paper, we present a numerical technique for solving fractional optimal control problems with a fractional derivative called Caputo–Katugampola derivative. This derivative is a generalization of the Caputo fractional derivative.
N. H. Sweilam, A. M. Nagy, T. M. Al-Ajami   +2 more
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Generalized Proportional Caputo Fractional Differential Equations with Noninstantaneous Impulses: Concepts, Integral Representations, and Ulam-Type Stability

Mathematics, 2022
The generalized proportional Caputo fractional derivative is a comparatively new type of derivative that is a generalization of the classical Caputo fractional derivative, and it gives more opportunities to adequately model complex phenomena in physics ...
Ravi Agarwal, Snezhana Hristova, Donal O’Regan   +2 more
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On Caputo Fractional Derivatives via Convexity [PDF]

Kragujevac Journal of Mathematics, 2020
Summary: In this paper some estimations of Caputo fractional derivatives via convexity have been presented. By using convexity of any positive integer order differentiable function some novel results are given.
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Extension of rate of change concept: From local to nonlocal operators with applications

Results in Physics, 2020
The concept of rate of change gave birth to numerous important theories and applications in mathematics, applied mathematics and other related academic disciplines.
Abdon Atangana
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Fractional hybrid systems involving '-Caputo derivative

Results in Nonlinear Analysis

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Chaos on the Vallis Model for El Niño with Fractional Operators

Entropy, 2016
The Vallis model for El Niño is an important model describing a very interesting physical problem. The aim of this paper is to investigate and compare the models using both integer and non-integer order derivatives.
Badr Saad T. Alkahtani, Abdon Atangana
doaj   +1 more source