Results 51 to 60 of about 47,231 (266)

Caputo derivatives of fractional variable order: Numerical approximations [PDF]

Communications in Nonlinear Science and Numerical Simulation, 2016
This is a preprint of a paper whose final and definite form is in Communications in Nonlinear Science and Numerical Simulation, ISSN: 1007-5704.
Tavares, Dina, Almeida, Ricardo, Torres, Delfim F. M.   +2 more
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A Nonlinear Implicit Fractional Equation with Caputo Derivative [PDF]

Journal of Mathematics, 2021
In this paper, we study a nonlinear implicit differential equation with initial conditions. The considered problem involves the fractional Caputo derivatives under some conditions on the order. We prove an existence and uniqueness analytic result by application of Banach principle.
openaire   +2 more sources

Fractional Herglotz variational principles with generalized Caputo derivatives [PDF]

Chaos, Solitons & Fractals, 2017
We obtain Euler-Lagrange equations, transversality conditions and a Noether-like theorem for Herglotz-type variational problems with Lagrangians depending on generalized fractional derivatives. As an application, we consider a damped harmonic oscillator with time-depending mass and elasticity, and arbitrary memory effects.
Garra R., Taverna G. S., Torres D. F. M.
openaire   +3 more sources

Fractional input stability for electrical circuits described by the Riemann-Liouville and the Caputo fractional derivatives

AIMS Mathematics, 2019
The fractional input stability of the electrical circuit equations described by the fractional derivative operators has been investigated. The Riemann-Liouville and the Caputo fractional derivative operators have been used.
Ndolane Sene
doaj   +1 more source

Analysis of fractional electrical circuit with rectangular input signal using Caputo and conformable derivative definitions [PDF]

Archives of Electrical Engineering, 2018
An analysis of a given electrical circuit using a fractional derivative. The statespace equation was developed. The dynamics of tensions described by Kirchhoff’s laws equations.
Ewa Piotrowska
doaj   +1 more source

Caputo-type modification of the Hadamard fractional derivatives [PDF]

Advances in Difference Equations, 2012
Abstract Generalization of fractional differential operators was subjected to an intense debate in the last few years in order to contribute to a deep understanding of the behavior of complex systems with memory effect. In this article, a Caputo-type modification of Hadamard fractional derivatives is introduced. The properties of the modified
Fahd Jarad, Thabet Abdeljawad, Dumitru Băleanu   +2 more
openaire   +3 more sources

Introduction to the fractional-order chaotic system under fractional operator in Caputo sense

Alexandria Engineering Journal, 2021
In this paper, we consider a new fractional-order chaotic system described by the Caputo fractional derivative. This paper’s main objective is to analyze the bifurcation maps to detect the chaotic regions for a new fractional-order chaotic system.
Ndolane Sene
doaj   +1 more source

Approximate Analytical Solution for Nonlinear System of Fractional Differential Equations by BPs Operational Matrices

Advances in Mathematical Physics, 2013
We present two methods for solving a nonlinear system of fractional differential equations within Caputo derivative. Firstly, we derive operational matrices for Caputo fractional derivative and for Riemann-Liouville fractional integral by using the ...
Mohsen Alipour, Dumitru Baleanu
doaj   +1 more source

On the existence of solutions for some infinite coefficient-symmetric Caputo-Fabrizio fractional integro-differential equations

Boundary Value Problems, 2017
By mixing the idea of 2-arrays, continued fractions, and Caputo-Fabrizio fractional derivative, we introduce a new operator entitled the infinite coefficient-symmetric Caputo-Fabrizio fractional derivative.
Dumitru Baleanu, Asef Mousalou, Shahram Rezapour   +2 more
doaj   +1 more source

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