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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 ...
The Mittag–Leffler function and its application to the ultra-hyperbolic time-fractional diffusion-wave equation
(Taylor & Francis Ltd, 2016-05)
In this paper we study an n-dimensional generalization of time-fractional diffusion-wave equation, where the Laplacian operator is replaced by the ultra-hyperbolic operator and the time-fractional derivative is taken in ...
Analysis of fractional-order models for hepatitis B
(2018-09-01)
This paper presents two models for hepatitis B, both given by fractional differential equations. The first model is formulated without parameters that indicate drug therapy, while the second one considers the drug therapy. ...
Boundedness of the solutions for certain classes of fractional differential equations with application to adaptive systems
(Elsevier, 2016)
This paper presents the analysis of three classes of fractional differential equations appearing in the field of fractional adaptive systems, for the case when the fractional order is in the interval alpha is an element ...
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 ...
An alternative definition for the k-Riemann-Liouville fractional derivative
(Hikari Ltd., 2015-01)
The aim of this paper is to introduce an alternative definition for the k-Riemann-Liouville fractional derivative given in [6] and whose advantage is that it is the left inverse of the corresponding of k-RiemannLiouville ...
Fractional Sobolev spaces with variable exponents and fractional p(X)-Laplacians
(Univ Szeged, 2017-11)
In this article we extend the Sobolev spaces with variable exponents to include the fractional case, and we prove a compact embedding theorem of these spaces into variable exponent Lebesgue spaces. As an application we ...
Optimal partition problems for the fractional Laplacian
(Springer Heidelberg, 2018-04)
In this work, we prove an existence result for an optimal partition problem of the form min{Fs(A1, …, Am) : Ai ∈ As, Ai ∩ Aj = ∅ for i ≠ j}, where Fs is a cost functional with suitable assumptions of monotonicity and lower ...
Comments on "Fractional order Lyapunov stability theorem and its applications in synchronization of complex dynamical networks"
(Elsevier, 2015)
© 2015 Elsevier B.V. This letter shows an incorrect application of the chain rule for fractional order derivatives reported in paper (Chen et al., 2014). Due to this misleading application, the proof of Theorem 2 and Theorem ...
Ground state solution for differential equations with left and right fractional derivatives
(Wiley & Sons, 2015)
In this work, we study the existence of positive solutions for a class of fractional differential equation given by
D-t(infinity-infinity)alpha D(t)(alpha)u(t) + u(t) = f(t,u(t)),
u is an element of H-alpha (R), ...