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Unexpected behavior of Caputo fractional derivative
(2017-09-01)
This paper discusses the modeling via mathematical methods based on fractional calculus, using Caputo fractional derivative. From the fractional models associated with harmonic oscillator, logistic equation and Malthusian ...
Global solution to a nonlinear fractional differential equation for the Caputo-Fabrizio derivative
(Natural Sciences Publishing, 2019-04)
In this article we prove existence and uniqueness of global solution to an initial value problem for a nonlinear fractional differential equation with a Caputo-Fabrizio (CF) derivative. We provide a new compact formula for ...
Explicit solutions to fractional Stefan-like problems for Caputo and Riemann–Liouville derivatives
(Elsevier Science, 2020-11)
Two fractional two-phase Stefan-like problems are considered by using Riemann-Liouville and Caputo derivatives of order α ∈ (0, 1) verifying that they coincide with the same classical Stefan problem at the limit case when ...
New Caputo-Fabrizio fractional order SEIASqEqHR model for COVID-19 epidemic transmission with genetic algorithm based control strategy
Fractional derivative has a memory and non-localization features that make it very useful in modelling epidemics’ transition. The kernel of Caputo-Fabrizio fractional derivative has
many features such as non-singularity, ...
Métodos numéricos para solução de equações diferenciais segundo a derivada de caputo
(Universidade Federal de Minas GeraisUFMG, 2015-12-16)
This thesis deals with the subject of non-integer order calculus mainly numerical methods or solving differential equations and dynamic systems analysis, according to the definition of the Caputo derivative.In this work, ...
An Euler-Lagrange Equation only Depending on Derivatives of Caputo for Fractional Variational Problems with Classical Derivatives
(International Academic Press, 2020-05-18)
In this paper we present advances in fractional variational problems with a Lagrangian depending on Caputo fractional and classical derivatives. New formulations of the fractional Euler-Lagrange equation are shown for the ...
Linear fractional differential equations and eigenfunctions of fractional differential operators
(2018-05-01)
Eigenfunctions associated with Riemann–Liouville and Caputo fractional differential operators are obtained by imposing a restriction on the fractional derivative parameter. Those eigenfunctions can be used to express the ...